For the purposes of "Continents" promotion it appears, as per Anne from Webflyer that flights can be credited to different oneworld programs. What's the best way to do this?

When I booked my flights then my TA asked for my frequent flyer number. If he enters this AAdvantage number for the whole trip then how can I put some flights into my BA EC membership? Now, don't get me wrong!! I am not trying to credit 2 different programs with the same flight but wouldn't BA raise the issue when I send them my boarding passes and they have AA number on them? Besides, wouldn't all flight segments go to my AA account automatically if AA number is used at the time of booking?