From The TimeSplitters Wiki

The flamethrower has appeared in both TS2 and TSFP. It shoots out a stream of flames that will start anyone who hits it on fire (in TSFP, it sometimes may not work.) In TS2. a character on fire would only go out when they stepped into water or rain. In TSFP, water also works, but it will go out eventually by itself. The flamethrower looks pretty much the same in both games, and never needs to be reloaded. It runs on Petrol, and a flamethrower uses up ammo similarly to an electrotool. I have found the flamethrower useful in story mode as it can automatically kill enemies quickly, especially when health is low.