According to Canfield US infantry weapons of WW2
The US had no flamethrowers during WW1 and had no interest between wars in flamethrowers. They began development of their first flamethrowers in 1940, so definitely not.
British and American infantry weapons of ww2 by Barker says this
"Flame throwers were not employed by the British infantry until 1943."
I would assume he considers the limited introduction of the Mk I in 42 as an unsuccessful trial. It was after all withdrawn from service.
Generally I think it is fair to say that without any evidence of their use, they should be withdrawn. The argument that they should be included because leftovers from WW1 might of been used seems to be drawing a bit of a long bow. I can find no evidence of flamethrower use outside the service dates I supplied. I did look.
And of course nearly all armies were in penny pinching mode between the wars. A flamethrower is a complex piece of equipment containing perishable seals etc, it needs regular pressure testing and maintenance you can't just leave it on the shelf for two decades and pick it up and expect it to not incinerate the operator. Someone has to remember how to service and use it and how to train others in its use all of which is very expensive, and unlikely. No doubt they were mostly scrapped.
My apologies for mistaking the Molotovs for one shot flamethrowers. I am guessing then that the Italian Lanciafiamme Mod 41 assalto is missing from the game, Probably would be a useful addition as it is available form 1941.
I did manage to find the German FmW.46 this time round, So to recap weapon 142 FmW.46 has a half second burst delivering 1.7 lt of fuel, This is equivalent to a burst from a normal manpack flamethrower, actually better than some. So it should have a HEKill much closer to 25. Game has HEKill of 15. It is a weapon specifically designed for Paratroop and infantry assault groups and later issued to volksgenadier. Not sure why it would get a HE penetration of 6 whereas a manpack flamethrower gets a HE penetration of 0. HEAT penetration and warhead size should probably be the same as for the manpack as well so changing from 6 and 5 to 14 and 45. The weapon gets 5 or 6 shots but is actually only capable of one shot.
This site
https://de.zxc.wiki/wiki/Einstossflammenwerfer_46
give production first date as Oct 44 but first use in Battle of Berlin. Appears in the game from 2/1945.