Flamethrowers are powerful weapons against infantry and tanks. They present the opportunity to effectively attack multiple (entrenched) units at the same time. Their blast radius is similar to grenades. (See table HE blast radius)
The attacker may use flamethrowers to set cover like buildings or woods on fire or destroy key structures like wooden bridges to keep the enemy from advancing. If the attacker intends to do so, no attack roll is needed. The attacker just has to spend one action on setting the target on fire.
Other than that, flamethrowers are handled like any other primary handheld weapon. They have a blast radius similar to grenades. So every unit in a radius of 5cm / 2in of the targeted unit has to check for a possible hit and effect. All units in the blast area have to check for morale.
If used against soldiers manning bunkers, no attack roll is needed. All soldiers in the bunker have to check for effect and morale.
However, flamethrowers do come with a restricted range of 40cm /16in.