"When bullets, shells, and explosives won't get the job done, burn it down!... Satan's own scalding hot shit-stick. Caliente!"
— Description in GTA CW.
It is a mechanical device designed to project a long controllable stream of fire. It is classified as a Heavy Weapon in the later editions. The Grand Theft Auto III rendition of the flamethrower is loosely based on the US Army M2 Flamethrower, albeit lacking a backpack fuel tank, and adopting a rifle-like design.
The renditions after GTA III are not based on any known flamethrower design, so it's assumed that they are homemade Flamethrowers, based on their fuel tanks and triggers however it's heatshield and part of the barrel appears to have been based on the barrels and heatshields from M2 Browning machine guns.
The flames from the flamethrower will only damage vehicles and pedestrians. In GTA San Andreas only, the flames can be created on the ground and can spread, making the fire extremely hard to put out if one is started with the flamethrower, even if only one little flame was made to start out with. The flames on the ground will not affect pedestrians but can affect vehicles and the player. If a pedestrian catches on fire, the pedestrian will usually run wildly until his or her death.
If you activate the flamethrower in front of a mirror, the fire will not show up on it.
Spoiler Warning:Plot and/or ending details are in the text which follows.
Harwood, Portland Island - On roof of the Head Radio building. It will be on a block-like object. This object is too high for the character to jump on, so you must plan accordingly in order to get there. A Hidden Package will be nearby. There is a video here
Hideouts - Available after extinguishing total 20 fires on each island in the Firefightervehicle mission. It should be noted the Flamethrower can be obtained very early in the game, provided the player get to Staunton Island by jumping the girder and steel beam on the broken Callahan Bridge (both left and right side). Since Shoreside Vale is not locked at this point the in game, the player can easily drive to it using either the Subway or the Porter Tunnel. He can then complete the 20 firefighting missions there, come back, do the same at Staunton before going back to Portland. This will make the Flame Thrower appear even if the player haven't completed any missions in Portland.
Viceport, Vice City Mainland - By the building near the road in the southwest part of Viceport, south of the Viceport Pay 'n' Spray. From the Viceport Pay 'n' Spray, head south along the road. As you near the road curve going east, you should see the weapon icon to your right.