I still think it should be forever unless you do one of the 3 things I suggested in the post above, but I like the extinguisher idea.
Maybe you can add the extinguisher to the medic class, and someone on fire would need the medic to use the fire extinguisher on them. That would be pretty neat. It would also increase teamwork, because if you dont work in a team, then you will burn to death.
Also, make a fireblanket. Basically, its an item that every class can use. When someone is about to burn you, you use the fire blanket, and then a gani shows of you rolling yourself on the floor with the blanket over you. This prevents you from getting burned (maybe make it so when the fire hits the blanket, it ends up 'splashing' the sides, to make it look like the blanket cant get hit by the fire, so instead the fire keeps going through the sides of the blanket.
NOTE: To make it more even for those which use flamethrower, when you want to disable the fire blanket, you will have to wait X amount of time until that is possible. That way, those using flamethrowers have enough time to load another gun or a knife, etc.
NOTE #2: If you are shot or stabbed by another weapon besides the flamethrower, then the fireblanket is immediately removed from you and/or destroyed (depends on whether you want to make it one of those items you need to constantly buy, or a permanent one).
This would be a pretty cool add-on

.