I am uncertain how you earned AAdvantage Miles on BA transatlantic flights as that is not permitted due to Anti_trust laws.
You cannot directly transfer AAdvantage Miles to BA Miles; however you could probably launder them through Hilton Hhonors or some such at a significant transaction cost.
Not worth doing that.
Except for MFU Upgrades, you can use AAdvantage Miles to redeem most (NOT transatlantic) BA flights, or any oneworld partner, though I think you would need to telephone AA to do this, and it would be prudent to check availability using your BA account first.
There are two options for transferring BA Miles between accounts; a direct transfer or setting up a household account. All this is fully explained in your BAEC homepage, for which login is required: