The Tesla Flamethrower is literally just a roofing torch like in [1] with a plastic gun around it and the valve turned all the way open. [2]
[0] https://upload.wikimedia.org/wikipedia/commons/transcoded/3/...
[1] https://www.youtube.com/watch?v=UprliuSNvX0
[2] https://qz.com/1191685/elon-musks-boring-company-flamethrowe...
Weeney propane torch: http://gigadgetstech.com/wp-content/uploads/2016/11/Organic_...
A real flamethrower: https://flamethrowerplans.com/wp-content/uploads/2016/03/Fla...
Or, as others have already described, one burns a flammable gas and puts out a flame a few inches long. The other squirts flammable liquid at you from a long ways away, then ignites it. </vast_oversimplification>
A flamethrower is essentially a gasoline/napalm hose / stream with a lighter at the end of it.