BA has said that they will not interline even their own flights if issued separately... eg CDG-LHR, LHR-JFK. You'd have to pick up your bags at LHR.

But CX will interline between KA and CX flights even issued on separate tickets, and on separate PNRs. CX will interline to other carriers if all the bookings are on the same PNR, eg Amadeus when on separate tickets.

Don't know what the others are gonna do.