1/4MM@20

That status alone does not get you in (unless you are GGL or CK on certain flights). So only access route would be a qualifying BA or AA flight in First. Since B6 is in a different terminal an international arrival would require clearing security in Terminal 8 without a boarding pass for a flight departing that terminal. I have heard conflicting reports on the feasibility of that over the years (never tried myself). So the only practical path I see would be a domestic arrival in T8 on a qualifying flight (LAX/SFO/SNA).

I suppose in theory you could have flown first on BA or Flagship First on AA to another US entry point and then a same day domestic connection to JFK (connecting to your onward B6 connection) and that would also get you access.