Imo the damage per second of flamethrowers is rather low and they are outgunned by even mediocre SMGs.
But keeping in mind issues the game had with flamethrowers and generally with flames, I suggest the following: damage amplification over time (yes, I stole this idea from a mobile game).
Basically the longer you are on fire, the more damage it does. This way stepping on a burning puddle won’t do much harm but standing in a jet of burning fuel will.
I imagine this as flame applying “burning” tag to the soldier, that stacks and adds +X% damage from fire per tag. Also the amount of those tags may affect how long it takes to be extinguished (it’s faster to put down a flame on your boot than on your whole person).
Thanks to this, flamethrowers (and flame in general) will be much deadlier but only when focused and not when spraying everything around