Also a reminder that do not use your AAdvantage number on AA bookings if you are planning to credit AA flights to BAEC in the future.
American wouldn't detach any AAdvantage number over a partner FFP, thus you shouldn't save any of your reservations to your AAdvantage account or use AAdvantage benefits when flying AA. This does not apply for BA flights but AA has a strict rule which doesn't allow cross-benefiting on their own flights.