The description for the green-flame blade spell (SCAG, p. 143) says:
As part of the action used to cast this spell, you must make a melee attack with a weapon against one creature within the spell's range.
It doesn't specify that the "attack with a weapon" can't be a "spell attack with a weapon".
Does the effect conjured by flame blade count as a weapon or not and therefore be used in conjunction with green-flame blade?
It doesn't say in the spell description of flame blade. It only states it is similar in size and shape to a scimitar which sounds strikingly like a weapon to me.
Best Answer
No
In fact, you can't even use a Flame Blade spell as part of an Attack (action).
The spell states:
The only mechanical uses of the the fiery blade are its unique action (make a melee spell attack, deal 3d6 fire damage on hit), and its ability to shed light.
Since you can't make a melee weapon attack with it, it isn't a weapon, and thus can't be used in conjuction with Green-Flame Blade.
Compare this to the spell Shadow Blade (from Xanathar's) which says:
The spell description specifically states that the effect counts as a weapon, and it defines the weapons properties.