I just recently used BA miles to claim an award on AA. I called up BA, gave them the info, said there was availability, and they'd make/confirm the booking with AA. I got a printed intinery in the mail, saying that I'd get the printed tickets about 4 weeks before travel date. Also something I didn't know, was that BA told me I can change the travel dates & times, without any charge for this award. (Not the cities of travel though.)