The most obvious one is to look on the AA site for AAdvantage MileSaver awards. The availability shown there should also be reflected on the BAEC redemption tool but there are some crazy things going on at the moment with that.

I had a problem today when looking for NYC-SFO availability. First of all I kept getting BA and its partners don't fly this route then after finally recognising that AA did all I got for weeks and weeks was zilch space then suddenly lots of seats - sometimes 7, appeared on just about every flight of the day which I thought was very strange.

The partner award search tool is very poor...no idea if it's BA's fault or a Oneworld one....a bit of both I suspect.