From my own experiences the flamethrower comes in handy in at least three different places:
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Oasis with the Allies - going through the lower tunnel at the very beginning of the match, and clearing out the flag room.
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Battery with the Allies/Axis - Keeping Axis forces away from the murder holes, and getting into/defending the choke point when entering the complex.
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Railgun with the Allies/Axis - useful for riding the train and flaming out to the sides, or flaming into the train to clear out an enemy passenger.
All weapons must be learned to a certain extent, its just that the learning curve for the flamer is a lot steeper.