I think that you are asking a slightly different question, Ro_Laren. You can book the BA flight with BA miles or AA miles. You don't transfer the miles from one program to another. If you book the BA flight with BA miles, you use the BA award chart to determine how many BA miles you need. If you book the BA flight with AA miles, you use the AA award chart to determine how many AA miles you need.

The award levels are different from carrier to carrier; thus if you have miles in multiple programs, you have the opportunity to optimize your mile spend for any given OW flight. Generally, all miles in OW carriers' programs are good for awards on all OW carriers. The cost varies, however, from program to program. And remember that the miles stay in their separate programs. You cannot combine miles from multiple programs to reach an award level.