You need to call to find out if they can even assign an AAdvantage number. Perhaps only AA itself can assign it, and if so you'll have to get one from AA and then you might have to give it to Barclays.

With two different banks (Citi and Barclays) issuing AA cards, I could imagine that AA might not let either of them assign AAdvantage numbers, because otherwise one bank would check with the other bank to make sure they didn't assign the same number to two different people!

Or, perhaps Barclays has to request a new number from AA, and who knows how long that takes.

So either way, you need to call and find out what the procedure and timing are.