The Turret could be used in a number of situations I would imagine. Obviously forest fire prevention is the ideal use case, but it could also be valuable for machine fires and fires within factory walls (which won't happen in vanilla, but a mod I use adds incendiary spitters).
I imagine it would work by having a larger effect radius then the flame turret, but also have a longer minimum range (further then the flame turret's minimum range where it cannot shoot close objects that is).
This way, placing a extinguisher turret behind a flame turret would result in an area where the flame turret can shoot, but the extinguisher cannot, where as at a further range again, the both the extinguisher and the flamer can shoot, and at the furthest range, the extinguisher has effect, but the flamer does not.
This would form an "effective range" where the flamer is free to burn, but if the flames spread to far out, they fall under the extinguisher's range, where they are promptly extinguished.
TL;DR, flamers can burn anything in its range, but if the fire spreads further then the range of the flamer, the extinguisher will put it out.