It is possible to enter a non-BA FFN when redeeming Avios for award travel. You would then get the elite benefits associated with the non-BA FFN when flying on BA flights.
If you are flying on airlines other than BA for your personal travel, you might well find that redeeming AA miles rather than BA Avios yields better value. AA does not collect any carrier surcharges on award redemptions, except when flying on BA or IB.
In addition, Etihad is an AAdvantage partner, but not a BAEC partner.