I don't use BA however I see an option to link to that travel program using my Amex Platinum Membership Rewards account to transfer miles.
Your request to link an account must be confirmed by your frequent traveler program.
This will take up to 5 days for domestic travel partners and up to 2 weeks for international partners.
Sadly AA isn't an option though there are some tricks to get from MR to AA. I think it's still possible to transfer to a hotel program like SPG and then into AA.