After making the Flamethrower, it needs to be filled with Hydrogen to run. Hook a Gas Tank up to an Electrolytic Separator and fill it with Hydrogen. Place the Flamethrower in the top slot and it should fill up relatively fast (<1 minute). Once full (24000 units of hydrogen) equip it and you should be set to go.
The flamethrower has pretty high damage and sets everything on fire. It also turns sand into glass.