Adding Skymiles number to KLM Flight Booked through AF with Flying Blue points?

Is this possible? I booked KLM flights using Flying Blue points on Air France's website. Since Delta is a Skyteam member, it looked like (from what I read online) that I might be able to add my Skymiles number to the booking, but it didn't allow me to via the AF website. The virtual agent I chatted with really didn't help and said to contact Delta, which doesn't necessarily make sense since the booking was through AF. Since I paid with Flying Blue points I know it might not actually be possible, but I'm wondering if anyone else has experience doing this? I will try to call AF at some point and speak to someone as well. The flight isn't until September so a ways out, I just had a few free moments this morning to play around with things.