Whilst they're the same 'physical flight' the flight number which will be on your ticket will be different; AAxxxx if booked on aa.com and BAxxxx if booked on BA.com. You can for a standard flight booking call up and ask to be booked on a codeshare. However, I have never been successful in getting BA Holidays to book an AA Codeshare for a flight and have tried probably three different times. BA Holidays are not 'BA' so to speak; they're a travel agents working on behalf of BA.

Good luck!