There isn’t really a reason to doubt a 37mm Hotchkiss She’ll would “fit” in a 37mm M8 flare gun. The match checks out… instantly. More modern flare guns tend to be smaller gauge than 37mm so if one assumed the M8 fired modern sized flares this mistake might make sense. More modern flare guns tend to be plastic, because flares are not high pressure rounds. Ever seen a flare gun fired, even in a movie? Did it zip out like a bullet or could you basically watch it lazily fly off? So even most metal flare guns aren’t designed to deal with high pressures of most projectile rounds. For this and other reasons, the problem isn’t wether the round fits but what would happen if you actually pulled the trigger. Which could be literally a click and nothing else or a big explosion right in your face.
As an asides, and I suspect most people know this but it bears saying- one should not generally put any amino ruin into a fire arm which the firearm is not designed to work with. There are special exceptions for people who REALLY know what they are doing, but in the world of guns and tools there are MANY examples of where a cartridge or shell can physically fit into a weapons firing chamber to the naked eye but attempting to fire, or in some cases even attempting to place the weapon into battery, can result in catastrophic failure which can kill or injure the person loading, firing, or even an innocent person minding their own business. The pressures generated by most charged projectiles and the explosive potential of most shells and cartridges can be extreme.
Be safe.
Be safe.