SEA->MIA->UIO FIRST/BUSINESS - flagship lounge?

1st leg AA2142 says FIRST, 2nd leg AA833 says BUSINESS. Nothing says FLAGSHIP.

Return LIM->MIA->SEA
AA1558 says BUSINESS, AA2363 says FIRST... again no FLAGSHIP in sight.

Not sure why they make it so complex but I think that doesn't count and I will be relegated back to the normal lounge. Don't want to get the SO excited for a special lounge if its not going to happen ;-)