If its on the same PNR and a connecting flight you will be able to check in for both on AA.com. That will allow you to have the boarding passes sent as a .pdf by email. Both boarding cards will be on the same .pdf if you are not printing you need to scroll down. You can either print that out or display on your phone which will get you through security and boarded on the AA flight. BA will need to see your passport before boarding either at the lounge or the gate and may reissue a boarding card.