Rehashing this thread, but my situation is a little different as I am on a domestic segment booked through BA.
I am flying SFO-LAX on AA (Envoy) with a BA flight number, which is the first segment of a BA ticket from LAX-LHR, currently in economy, is there anyway to receive a complimentary upgrade (<500 miles) on this segment or is it not possible since I booked through BA and the flight has a BA flight #?