The USA number.
1-800-AIRWAYS
which is
1-800-247-9297
and is open to 01:00 hrs Eastern.
You want the change booking option
It's a great idea to memorise this, since you can find almost all numbers this way:
ba.com/contact-us
If AA just need your BA ticket number, and they have a sync issue, you can give them this via the App, via the Flight Details panel, towards the bottom, starting 125. If that number is not there, then AA can do nothing, it's over to BA.