My understanding is that extra luggage allowance is airline specific. If you're on a multi-airline trip, other airlines don't have to honour your extra allowance and can subject you to extra luggage charges.

In your case, if you're AA Plat, your CX trip probably won't allow you any extra luggage.

I'm a QF Gold, and had a BA/QF trip. I asked whether my extra allowance will carry through, the answer was 'no'.