If you are in F on BA you can use the Flagship Lounge and FFD, this area is in the D concourse.

BA board from the E concourse which is a short tram ride away but you only need to go there when you want to go to the gate.
All the concourses are connected so you wouldn't need to re-clear security.
My experience as a GGL in F is that they will escort you to security and if you have TSA Pre they will put their little sign in with your luggage.