It depends on the maneuver. Menacing Attack requires a weapon attack, so Green Flame Blade qualifies. Commander's Strike requires an Attack Action, so you would not be able to combine it with GFB. And Feinting Attack grants advantage on your next Attack Roll, so you could even combine this with Eldritch Blast since EB requires an Attack Roll to hit.
Since you can choose the second creature, most DMs I know rule that it fizzles out. Otherwise the warlock starts carrying a bag of rats, so they can cast GFB without hurting themselves... But you could also rule that the fire hurts the warlock if no other creature is available.
When using the Green Flame Blade cantrip to make a melee attack can the Battle Master superiority die still be added to the hit?
example 3 Fighter/2 warlock with 16 charisma and a war hammer
war hammer 1d8
Green Flame blade (at lvl 5, ignoring the damage to the second creature here) 1d8
Menacing attack 1d8
ending up with a 3d8+3 attack to initial target?
also if you don't select a second creature for the flame to jump to, does it just fizzle out or do shenanigans arise?
It depends on the maneuver. Menacing Attack requires a weapon attack, so Green Flame Blade qualifies. Commander's Strike requires an Attack Action, so you would not be able to combine it with GFB. And Feinting Attack grants advantage on your next Attack Roll, so you could even combine this with Eldritch Blast since EB requires an Attack Roll to hit.
Since you can choose the second creature, most DMs I know rule that it fizzles out. Otherwise the warlock starts carrying a bag of rats, so they can cast GFB without hurting themselves... But you could also rule that the fire hurts the warlock if no other creature is available.