Pretty much all BA shorthaul flight operate from Pier 6 at times with the exception of the internal Shuttle services, the occasional long haul uses it too. Lot's of the GeeBee flights use it on some rotations..
From a not too keen an observer’s position there does not seem to be any set pattern as to which flights use the gates on Pier 6.
For a guaranteed pier 6 departure try the Etihad.