I believe wemyss is suggesting that you collect AA miles rather than BA miles. The only way to convert AA miles to BA is an intermediate transfer to Hilton HHonors and you would lose 80% of the value in process...

AA 5,000 miles
HH 10,000 points (pay $30 fee)
BA 1,000 miles

AA and BA are both members of the OneWorld alliance. You cannot transfer miles from one OneWorld member to another, but you can redeem for travel on other OneWorld members. However, there is one specific exclusion due to antitrust concerns. You cannot cross earn or cross redeem AA/BA miles on flights between the UK and the USA. For example, you could fly between the UK and Canada on a BA flight and earn or redeem miles in the AA program, but you cannot do this between the UK and the USA.