Going into The Winds of Winter, we probably can expect to witness the Golden Company taking Storm's End by "guile" in TWOW, Jon Connington I and then the subsequent negotiations with Dorne in TWOW, Arianne III.

After that we should expect to see fAegon face off against Mace Tyrell in a battle outside Storm's End.

Mace Tyrell vs. fAegon and the Golden Company

There is an army descending on Storm’s End from King’s Landing. You will want to be safe inside the walls before the battle.”

Will we? Wondered Arianne. “Battle? Or siege?” She did not intend to let herself be trapped inside Storm’s End.

“Battle,” Halden said firmly. “Prince Aegon means to smash his enemies in the field. -TWOW, Arianne II

Tyrell Strength/Approach

Strength

There are 50,000 to 70,000 Tyrell swords in King's Landing:

"Then take a good sniff, my lord. Fill up your nose. Half a million people stink more than three hundred, you'll find. Do you smell the gold cloaks? There are near five thousand of them. My father's own sworn swords must account for another twenty thousand. And then there are the roses. Roses smell so sweet, don't they? Especially when there are so many of them. Fifty, sixty, seventy thousand roses, in the city or camped outside it, I can't really say how many are left, but there's more than I care to count, anyway." -ASOS, Tyrion V

Mace Tyrell had besieged Storm's End with half the Tyrell forces, but left to deal with Margaery's trial, leaving Mathis Rowan with a small force to maintain the siege.

Mace is taking half the Tyrell strength to Storm's End, and the other half will be going back to the Reach with Ser Garlan to make good his claim on Brightwater. A few more days, and the only roses left in King's Landing will be Margaery and her ladies and a few guardsmen." -AFFC, Cersei III

So with that in mind, Mace likely has between 25,000 and 35,000 men to march on Storm's End.

Approach

Mace is way overconfident, especially for someone who doesn't seem to have succeeded much in the way of warfare:

Robb Stark had won more battles in a year than the Lord of Highgarden had in twenty. Tyrell's reputation rested on one indecisive victory over Robert Baratheon at Ashford, in a battle largely won by Lord Tarly's van before the main host had even arrived. The siege of Storm's End, where Mace Tyrell actually did hold the command, had dragged on a year to no result, and after the Trident was fought, the Lord of Highgarden had meekly dipped his banners to Eddard Stark. -ASOS, Tyrion III

And little respect:

Randyll Tarly left the hall with his liege lord, their green-cloaked spearmen right behind them. Tarly is the real danger, Ser Kevan reflected as he watched their departure. A narrow man, but iron-willed and shrewd, and as good a soldier as the Reach could boast. But how do I win him to our side? -ADWD, Epilogue

and:

"… as for Connington," Tyrell repeated, "what victories has he ever won that we should fear him? He could have ended Robert's Rebellion at Stoney Sept. He failed. Just as the Golden Company has always failed. Some may rush to join them, aye. The realm is well rid of such fools." -ADWD, Epilogue

and:

To the south, meanwhile, Mace Tyrell had raised a city of tents outside Storm's End and had two dozen mangonels flinging stones against the castle's massive walls, thus far to small effect. Lord Tyrell the warrior, the queen mused. His sigil ought to be a fat man sitting on his arse.

and:

"Storm's End." Lord Mace Tyrell grunted the words. "He cannot take Storm's End. Not if he were Aegon the Conqueror. And if he does, what of it? Stannis holds it now. Let the castle pass from one pretender to another, why should that trouble us? I shall recapture it after my daughter's innocence is proved." -ADWD, Epilogue

​

Golden Company Strength/Approach

The Golden Company is made up of 10,000 men:

"The Golden Company is the best and largest of the free companies, but ten thousand mercenaries cannot hope to win the Seven Kingdoms. -TWOW, Arianne I

Which includes 500 knights:

We have ten thousand men in the company, as I am sure Lord Connington remembers from his years of service with us. Five hundred knights, each with three horses. Five hundred squires, with one mount apiece. And elephants, we must not forget the elephants. -ADWD, The Lost Lord

At least 2 dozen elephants:

They found the Golden Company beside the river as the sun was lowering in the west. It was a camp that even Arthur Dayne might have approved of—compact, orderly, defensible. A deep ditch had been dug around it, with sharpened stakes inside. The tents stood in rows, with broad avenues between them. The latrines had been placed beside the river, so the current would wash away the wastes. The horse lines were to the north, and beyond them, two dozen elephants grazed beside the water, pulling up reeds with their trunks. Griff glanced at the great grey beasts with approval. There is not a warhorse in all of Westeros that will stand against them. -ADWD, The Lost Lord

1,000 Archers under Black Balaq:

Black Balaq commanded one thousand bows. In his youth, Jon Connington had shared the disdain most knights had for bowmen, but he had grown wiser in exile. -ADWD, The Griffin Reborn

which is made up of 1/3 crossbows, 1/3 Essosi bows, 1/4 Westerosi longbows and 50 goldenheart bows:

A third of Balaq's men used crossbows, another third the double-curved horn-and-sinew bows of the east. Better than these were the big yew longbows borne by the archers of Westerosi blood, and best of all were the great bows of goldenheart treasured by Black Balaq himself and his fifty Summer Islanders. Only a dragonbone bow could outrange one made of goldenheart. Whatever bow they carried, all of Balaq's men were sharp-eyed, seasoned veterans who had proved their worth in a hundred battles, raids, and skirmishes. They proved it again at Griffin's Roost. -ADWD, The Griffin Reborn

But the company is scattered after Lys due to storms:

The damned Volantenes are so eager to be rid of us they are dumping us ashore on any bit of land they see," said Franklyn Flowers. "I'll wager you that we've got lads scattered all over half the bloody Stepstones too." -ADWD, The Griffin Reborn

and so far only about the half the company has shown up:

Ten thousand men had sailed from Volon Therys, with all their weapons, horses, elephants. Not quite half that number had turned up thus far on Westeros, at or near their intended landing site, a deserted stretch of coast on the edge of the rainwood … lands that Jon Connington knew well, as they had once been his.

Six out of the ten ships with archers have appeared:

In its own way, the arrow was as deadly as the sword, so for the long voyage he had insisted that Homeless Harry Strickland break Balaq's command into ten companies of one hundred men and place each company upon a different ship.

Six of those ships had stayed together well enough to deliver their passengers to the shores of Cape Wrath (the other four were lagging but would turn up eventually, the Volantenes assured them, but Griff thought it just as likely they were lost or had landed elsewhere), which left the company with six hundred bows. For this, two hundred proved sufficient. "They will try to send out ravens," he told Black Balaq. "Watch the maester's tower. Here." He pointed to the map he had drawn in the mud of their campsite. "Bring down every bird that leaves the castle." -ADWD, The Griffin Reborn

They split the forces up in order to take more castles, but are still low on horses/elephants:

"By this time on the morrow we ought to hold three castles," he said. The force that had taken Griffin's Roost represented a quarter of their available strength; Ser Tristan Rivers had set off simultaneously for the seat of House Morrigen at Crow's Nest, and Laswell Peake for Rain House, the stronghold of the Wyldes, each with a force of comparable size. The rest of their men had remained in camp to guard their landing site and prince, under the command of the company's Volantene paymaster, Gorys Edoryen. Their numbers would continue to swell, one hoped; more ships were straggling in every day. "We still have too few horses."

"And no elephants," the Halfmaester reminded him. Not one of the great cogs carrying the elephants had turned up yet. They had last seen them at Lys, before the storm that had scattered half the fleet. "Horses can be found in Westeros. Elephants—" -ADWD, The Griffin Reborn

They take several locations relatively easily (Griffin's Roost, Crow's Nest, Rain House, Estermont, Tarth and half the Stepstones):

The castle rose from the shores of Cape Wrath, on a lofty crag of dark red stone surrounded on three sides by the surging waters of Shipbreaker Bay. Its only approach was defended by a gatehouse, behind which lay the long bare ridge the Conningtons called the griffin's throat. To force the throat could be a bloody business, since the ridge exposed the attackers to the spears, stones, and arrows of defenders in the two round towers that flanked the castle's main gates. And once they reached those gates, the men inside could pour down boiling oil on their heads. Griff expected to lose a hundred men, perhaps more.

They lost four. -ADWD, The Griffin Reborn

and:

"Word's reached the camp from Marq Mandrake. The Volantenes put him ashore on what turned out to be Estermont, with close to five hundred men. He's taken Greenstone." -ADWD, The Griffin Reborn

And as we can see, numerous men/elephants have arrived, just haven't met the main force:

"Tarth has fallen too, some fisherfolk will tell you," said Valena. "These sellswords now hold most of Cape Wrath and half the Stepstones. We hear talk of elephants in the rainwood."

"Elephants?" Arianne did not know what to think of that. "Are you certain? Not dragons?" -TWOW, Arianne I

and:

“Is it true that you have elephants with you?”

“A few,” said Lysono Maar, with a smile and a shrug. -TWOW, Arianne II

fAegon arrives with 100 mounted men and 3 elephants:

The prince arrived to join them four days later, riding at the head of a column of a hundred horse, with three elephants lumbering in his rear. Lady Lemore was with him, garbed once more in the white robes of a septa. Before them went Ser Rolly Duckfield, a snow-white cloak streaming from his shoulders. -ADWD, The Griffin Reborn

Mangonels

They may have taken the mangonels from Mathis Rowan when they took Storm's End:

To the south, meanwhile, Mace Tyrell had raised a city of tents outside Storm's End and had two dozen mangonels flinging stones against the castle's massive walls, thus far to small effect. Lord Tyrell the warrior, the queen mused. His sigil ought to be a fat man sitting on his arse.

Approach

The Golden Company is vastly outnumbered, that said, they are seasoned warriors:

Fortunately his own ship had been one of the first to reach their destination. Then it had only been a matter of establishing a campsite, assembling his men as they came ashore and moving quickly, before the local lordlings had any inkling of their peril. And there the Golden Company had proved its mettle. The chaos that would inevitably have delayed such a march with a hastily assembled host of household knights and local levies had been nowhere in evidence. These were the heirs of Bittersteel, and discipline was mother's milk to them. -ADWD, The Griffin Reborn

JonCon has gain experience (which Mace Tyrell doesn't seem to recongnize):

That was all so long ago, though. If this is indeed Jon Connington, he will be a different man. Older, harder, more seasoned … more dangerous. "Connington may have more than the Golden Company. It is said he has a Targaryen pretender." -ADWD, Epilogue

Dornish thoughts:

“Whoever’s son he is, if Connington challenges Mace Tyrell in open battle he may soon be a captive, or a corpse.”

“Tyrell is not a man to fear. My uncle Oberyn–”

“ –is dead, princess. And ten thousand men is equal to the whole strength of the Golden Company.”

“Lord Connington knows his own strength, surely. If he means to risk battle, he must believe that he can win it. -TWOW, Arianne II

Support for the GC

Even with Lord Puff Fish leading the Tyrell force, the GC is still vastly outnumered and if they are to win, they will need support.

They expect some support:

"I thought the crossbow fitting. You shared so much with Lord Tywin, why not that? Your niece will think the Tyrells had you murdered, mayhaps with the connivance of the Imp. The Tyrells will suspect her. Someone somewhere will find a way to blame the Dornishmen. Doubt, division, and mistrust will eat the very ground beneath your boy king, whilst Aegon raises his banner above Storm's End and the lords of the realm gather round him. -ADWD, Epilogue

and:

Laswell Peake rapped his knuckles on the table. "Even after a century, some of us still have friends in the Reach. The power of Highgarden may not be what Mace Tyrell imagines." -The Lost Lord

and:

"Not yet. Let King's Landing think this is no more than an exile lord coming home with some hired swords to reclaim his birthright. An old familiar story, that. I will even write King Tommen, stating as much and asking for a pardon and the restoration of my lands and titles. That will give them something to chew over for a while. And whilst they dither, we will send out word secretly to likely friends in the stormlands and the Reach. And Dorne." That was the crucial step. Lesser lords might join their cause for fear of harm or hope of gain, but only the Prince of Dorne had the power to defy House Lannister and its allies. "Above all else, we must have Doran Martell." -The Lost Lord

And others assume they will get some as well:

Land and raise your banners, and men will flock to your cause. Lords great and small, and smallfolk too. But do not wait too long, my prince. The moment will not last. The tide that lifts you now will soon recede. Be certain you reach Westeros before my sister falls and someone more competent takes her place." -ADWD, Tyrion VI

and:

Stannis is too far away to be of help to him,” Arianne mused. “Capturing a few minor castles whilst their lords and garrisons are off at distant wars, that’s one thing, but if Lord Connington and his pet dragon can somehow take one of the great strongholds of the realm …”

“…the realm would have to take them seriously,” Ser Daemon finished. “And some of those who do not love the Lannisters might well come flocking to their banners.” -TWOW, Arianne II

Dorne

Dorne is a very possible/if not likely option for an alliance with the Golden Company. Due to the fact that they basically won't be able to ally with Dany (due to Quentyn), and want revenge on the Lannisters, it makes some sense:

Preparations should be made for Princess Myrcella."

"This is what comes of dealing with the Dornish," Mace Tyrell said. "Surely a better match can be found for the girl?"

Such as your own son Willas, perhaps? Her disfigured by one Dornishman, him crippled by another? "No doubt," Ser Kevan said, "but we have enemies enough without offending Dorne. If Doran Martell were to join his strength to Connington's in support of this feigned dragon, things could go very ill for all of us."

If interested: Arianne's Negotiations with JonCon/fAegon at Storm's End

The Dornish have armies in the Boneway and the Prince's Pass as well.

Other Houses

If interested: List of Known Past Blackfyre Supporters

Possible Other Support

The town was large enough to support three inns, and all their common rooms were rife with rumors. Arianne sent her men into each of them, to hear what they might hear. In the Broken Shield, Daemon Sand was told that the great septry on the Holf of Men had been burned and looted by raiders from the sea, and a hundred young novices from the motherhouse on Maiden Isle carried off into slavery. In the Loon, Joss Hood learned that half a hundred men and boys from the Weeping Town had set off north to join Jon Connington at Griffin’s Roost, including young Ser Addam, old Lord Whitehead’s son and heir. But in the aptly named Drunken Dornishman, Feathers heard men muttering that the griffin had put Red Ronnet’s brother to death and raped his maiden sister. Ronnet himself was said to be rushing south to avenge his brother’s death and his sister’s dishonor. -TWOW, Arianne II

Hostages

In addition to characters like Mathis Rowan and even Arianne being potentially considered as hostages, we also see:

Arianne's thoughts went at once to her sweet Spotted Slyva. "Who would want Greenstone? Was there a battle?" -TWOW, Ariane I

and it should be noted that Red Ronnet is expected to have marched with Mace to Storm's End:

By the time Connington made his descent, his men had gathered the castle garrison and surviving smallfolk together in the yard. Though Ser Ronnet was indeed off north somewhere with Jaime Lannister, Griffin's Roost was not quite bereft of griffins. Amongst the prisoners were Ronnet's younger brother Raymund, his sister Alynne, and his natural son, a fierce red-haired boy they called Ronald Storm. All would make for useful hostages if and when Red Ronnet should return to try and take back the castle that his father had stolen. Connington ordered them confined to the west tower, under guard. The girl began to cry at that, and the bastard boy tried to bite the spearman closest to him. "Stop it, the both of you," he snapped at them. "No harm will come to any of you unless Red Ronnet proves an utter fool." -ADWD, The Griffin Reborn

The Stepstones

The current situation in the Stepstones is a mess, but it should be noted that the Golden Company has taken "half the stepstones":

These sellswords now hold most of Cape Wrath and half the Stepstones.

with that in mind, the number of possibilities for support for fAegon grows quite a bit to potentially include:

• Aurane Waters
• Salladhor Saan
• Edric Storm

Conclusion

As I mentioned, I expect fAegon to take King's Landing and some point and therefore winning this battle is a necessity. I expect some outside support from one or more of the groups listed above.

I originally didn't intend to make this a multipost subject, but this post does follow the previously linked posts about the initial attack on Storm's End and the meeting with Arianne.

TLDR: fAegon is going to get some outside support and smash an overconfident Mace Tyrell outside of Storm's End on his way to King's Landing.