If on the one PNR, BA will provide the most generous allowance for the passeger on their itinerary.

If on the one itinerary (can be more than one PNR) for international travel, Qantas will allow up to two pieces at 32/23Kg (depending upon travel class) if the itinerary includes travel via the pacific.

If on the one itinerary (can be more than one PNR) American will allow checked baggage greater than their standard or not charge fees in some cases.

But, no, other than BA there no alliance check baggage benefit. With BA this is only applicable if your PNR includes travel on you 'home' program's carrier where you get that extra allowance.