Originally Posted by
Madison Guy
True, but since OP already stated the flight is AA51, there is zero possibilty of it being operated by BA. But I believe your point is that award tickets must always be booked on the operating carriers flight number - not a codeshare. (Oddly enough, I can't get AA.COM to offer any reward BA flights on several days I tried for LHR/LAX or LHR/DFW. Often I can't find AA flights!)
At least for LHR-DFW, BA isn't flying LHR-DFW during their summer schedule, so depending on what dates you looked that might be why.