Whichever airline you fly just always make sure your BA FF number is on the booking for the TP's to credited to BAEC to get them and the Avios.

Are they AA flights, booked on AA with a BA prefix? Or BA booked with a BA prefix and AA flights?

If so you can do this in the AA website record locator where there is a drop down for your BA FF number to be added. Alternatively and the old fashioned way you can just call them and ask them to do it for you. And welcome to Flyertalk and the BA Board biertje