I will have to disagree.
Flamethrowers usually use some kind of liquid fuel (for example Napalm) and usually that liquid fuel contains gasoline or other oil derivative. Since the resource war happened because there was not much oil left in the world(the USA even stop using helicopters, tanks and airplanes because it run out of fuel for them) and armies all over the world were developing energy weapons (laser and plasma) because it would use energy ammo instead of relying on the old wasteful ammunition. I don't see them having enough fuel for making so many "long-range flamethrowers" when the laser weapons were purposefully made to save resources and were a priority of weapon research by the USA.