One would think that in space even a plasma flamethrower's range would be lower
Well, no. You see, space has a few things missing. Things which traditionally "gimp" a flamethrower.
An atmosphere and gravity.
No atmosphere? No friction and nowhere for the thermal energy to disperse to (thereby, the round has a longer active "life-time" because long after the thermic reaction that heats the material, it cannot cool and remains useful plasma).
No friction? Infinite range, in terms of the actual mass, until it hits something.
Very little gravity in relevance to the round's trajectory?
Again, range is potentially infinite and effective up to and around 500 feet or more. And if it's magnetically accelerated? You're looking at hundreds of kilometers, as an effective weapon.
The issue then becomes ammunition but this could be solved with automatic for close-quarters and single shot/burst for ranged attack, identical to a real rifle or carbine.
Only with white hot death at 2000 kelvin upwards or so, instead of a hail of inaccurate rounds at melee ranges.
FISH would never be the same again.