The 16-bit era is about as far back as I can remember seeing flamethrowers in video games. Titles like Super Contra, Gouls'n'Ghosts, and Mystic Defender would all treat jets of fire like a wobbly chain made of interconnected sprites that would steadily inflict damage on anything caught in its path. An admirable first effort, but still a long way from, the real thing. Gain Ground is another slightly different 16-bit example. One of the playable units was capable of using a flamethrower which would fart out short range slow moving balls of fire. Provided you could mash the attack button like crazy, it was possible to get something resembling a steady stream of flame. Sadly, it never really had a good in-game use. One final 16-bit game that had yet another take was Alien 3. While not consistent with the film of the same name, it was possible to get an incinerator unit that would spurt out pre-rendered gouts of fire considerable distances. While an improvement over anything which had come before, it still lacked the ability to ignite other objects in the environment, nor did the xenomorphs seem at all intimidated by it.
Of course in the world of video games safety isn't exactly a high priority. After playing through The Last of Us, I found myself rather pleased with the way the jerry-rigged flamethrower and Molotov cocktails worked. Granted the range for the former is a still a bit short, but at least they got the effect right. Enemies in particular, react with horrific accuracy when burned, and best of all (or worst, depending on your perspective) ballistic armor and cover confer no benefit. Regrettably, you still can't ignite stuff in the game environment. I guess that's asking a bit much for current gen consoles though. Regardless, I hope someone tries to make a realistic firefighting sim someday. Maybe base it in pre-modern Japan with the player managing an Edo (now Tokyo) based unit of Hikeshi. That would be cool...er...maybe I should say hot? Well, you know what I mean.