BA transatlantic T-class fares and AA domestic KUP-type fares are normally combinable so it should be feasible and should cost in the region of £1400 for your itinerary, as long as there is availability in the relevant classes (T for the BA flights and P for the AA flight). You need a live agent to do that, though, so either call BA or AA or a travel agent, specifying that you want the tatl legs in T and the AA leg in P.

Fares bases should be (BA) TKX3UKJB for the tatl legs and (AA) KA7UPPDN for the domestic leg. Note, though, that the KUP fare on SFO-LAX is not especially cheap at nearly $400++ oneway.