Are you looking for BA flights are partner airline flights? If you are looking for AA flights, there are any number of threads (including the Guide to Spending Avios sticky at the top of the forum) where it is recommended to search aa.com to see if you can find milesaaver availability. If you find milesaaver availability then you should be able to find the same availability on ba.com. If you can't find it on ba.com (usually because it involves connecting flights on partner airlines) then you should search for the connecting flights individually and either book them individually on ba.com or call and book them together.

You cannot transfer a reward reservation from AA to BA.