What about a .30-caliber rifle with an underslung flamethrower? Flamethrower is connected to a plated fuel tank designed to be mounted below a soldier's pack, and there are two triggers: one for the .30 cal and one on for the flamethrower.
A miniature flamethrower like that would be complicated, and still probably require a backpack for fuel. Probably better to get a working flamethrower at all first. Furthermore, so far you've been using rifles for long engagements, and sidearms (swords, shotguns and revolvers) for close engagements. Your soldiers don't usually have rifles in hand in trenches.
Work on the Flamethrower begins.
Moskurg Flamethrower: This consists of two tanks, and a nozzle, connected in series by rubber hoses. The first tank is filled with pressurized air, and the second with fuel. The soldier wielding it controls a valve which, when opened, causes the pressurized air tank to force fuel out of the nozzle. The pilot light is a simple burning torch. It has a very short range, of about 15 feet, and the fuel lasts for about a minute of fire. Its design is complicated, making it Expensive, but you have enough fuel to deploy it often. Throughout testing the weapon suffers a number of complete disasters, from the valve being stuck open, to tanks and hoses rupturing. The building where the flamethrowers were being built burned down. This weapon was a complete and abject failure, and will require another design phase.
You've gain the technology: Flamethrower [Partially Complete]. This is not useful on its own but will make it easier next time. For clarity, this result was caused both by rolling a 1, and another factor.
You may now revise something.