The flame on Monkarp's tail is usually unlit and is only used to intimidate other Pokémon. In reality, the flame is incapable of causing any substantial burns, and it takes a great deal of Monkarp's energy to keep it lit for even a few seconds.
Its swimming muscles are weak, so it is easily washed away by currents. To intimidate attackers, it stretches the fire on its tail to make itself appear bigger.