You also need four qualifying flights on BA to qualify for BA Silver. So flying on AA alone would not be sufficient since you only get 2 BA flights on this route.

Must you fly BA? You could choose AF, DL to LHR and then take AF to NRT
There is a AA direct flight from LAX to LHR or from SFO there are connections via ORD on AA or ATL on DL.
The choice is then AF to NRT from Paris. You can either fly AF from LHR and connect or if you have time, take the Eurostar for a change.