You will get Avios and Tier Points on your flights.

There needs to be A class availability on the JAL flights for you to book on them. It is up to the airline if they release A seats on flights. You could try other dates or a different routing (add an AA sector to ORD or LAX) and see if JAL have A availability on flights from those cities on the dates you need.
You could also book the AA flight and hope that JAL will open up A on the flight you want and make the change then. Of course this could be risky if they don't open up any A class.