Flames of Phlegethos works for cantrips too.
There is no spell level restriction mentioned in the feat description, so Flames of Phlegethos works just the same for cantrips as it does for leveled spells; the feat description says:
for a spell you cast
And
whenever you cast a spell
Cantrips are spells - from the rules for cantrips:
A cantrip is a spell.
So cantrips qualify for the feat if they deal fire damage - which green flame blade does.