There are some FFM tie-ups between BD and VS. I score VS miles on BD flights and can redeem for BD and have been able to do so for a number of years. I don't know if it's the same in reverse but presume so.
I agree that a formal tie up would get BA/AA out of their pram very quickly! Personnally, I have always thought that the two would make a good partnership but their styles and history are so different that it would be unlikely to work.