This is a possible bug or possibly not fully implemented yet.
Using Alt fire (charged shots) with Drakefire Flamethrower or Pistols, and the Heat Sink Trait, doesn’t seem to change how much Overcharge is generated.
It does work with the primary fire (left click).
Additional:
It doesn’t seem to work with any of the Flamethrowers on any of the Careers, PERIODT. @FatsharkJulia