I had some similar problems on a paid BA ticket, and even entering the BA record locator did not help since it did not recognize the AA status.
After calling BA's elite line, they changed something so I finally had assigned seats and could see them, but could not change them. So, IME, their system is not perfect in dealing with this kind of situation. I finally just gave up, but did wind up with decent seats.
I could give you a long list of other reasons to avoid BA, but that wasn't the question.