Your question deals with redeeming Avios and is best dealt with in the BA forum. That said, you can only redeem avios by booking with BA, either by phone or on ba.com. You cannot redeem avios on aa.com or with any other airline.

You haven't said what dates you are trying to book but it is possible that the availability is gone. If you want to avoid the high fuel surcharges with BA then redemptions on EI or AB are good for that. EI is not a member of the oneworld alliance and its reward availability is not shown on ba.com. You have to call to check. You may want to review the Guide to Spending Avios here:
http://www.flyertalk.com/forum/briti...os-2015-a.html

Considering your lack of familiarity with the BAEC and your desire to not redeem for flights on BA, you might just be better off redeeming your Avion points as is.