Originally Posted by jerry a. laska

No. Only AA milesaaver availability is bookable by BA and other partners. Also, ba.com often has trouble displaying milesaaver availability involving connections and when there are many flights each day between cities. Sometimes there is availability and you just need to call. See, for example, the discussion earlier in this thread and the threads listed therein:
https://www.flyertalk.com/forum/32929430-post14.html