Do you mean getting a seat reservation at checkin time, or doing so beforehand because you have some sort of status with BA? EIther way you should find that BA's online system gives you access to AA's system to do the seat reservation. Go to Manage My Booking, then choose that segment, then choose seating and it will take you to the AA site to accomplish it. I've done that just a few days ago for a flight back SFO-ORD-LHR-EDI where the first segment is AA.

it did set some strange cookied in my browser which stoppped the BA site displaying correctly once I had done the seat assignment but closing and reopening the browser fixed that.