Simple answer: If it is shown on the other carrier's FF website as available, it is more often than not available to AA for award booking.

Many others have had more experience with CX/KA's issues, I have booked mostly JL group tickets from AA miles recently.

If you look at JMB's award system (account needed), you will see that they have an option for "waiting list" on JAL group award flights. Those flights are always unavailable for award inventory to AA miles, unless the inventory is opened up later (which happens moderately often).

The kicker for this is that if the plane is pretty full, they will also clear waiting lists before adding more award inventory as well. This can be tough for AA flyers on high-demand routes as a result. But even so, I have often found the award inventory I wanted in the end, but often switching the ticket date as award inventory became available.