Flaming archers are heavy archer-variants, specialising as anti-siege units. They use arrows that are set on fire. This allows them to have anti-vehicle higher attack. They are armed and armoured to return a volley of fire against any enemy ranged infantry, as part of a two-wave engagement and are also slower and heavier; but their higher expense is largely wasted against cavalry or melee infantry.
Unlike their skirmisher anti-infantry counterparts, the light Re-Curve Bowman, the Flaming Archers are slower and heavier armed. Their primary purpose is to fire upon the remains of the enemy ranged section, after the artillery have fired, and take out any remaining units. Their increased anti-vehicle damage enables them to take out an extra standard siege unit, or one polybolos between two archers.
It is best to pair these units with a decent anti-infantry artillery component to eliminate the enemy's ranged section before they can fire, as all ranged/archer units fire simultaneously, and taking archer losses will severely reduce your army's second-round capability.
Their armour allows them to return a second volley stronger than the other archers (although it is still much weaker than if the archers had not been targeted).