The Man on Fire is invulnerable to conventional weapons. Your strategy must focus on environmental hazards. In the first encounter, you must escape. In later encounters, you can use water towers, fire extinguishers, or even a water pistol to temporarily incapacitate him. Once stunned, you can Fulton him or use heavy weapons to deal damage while he's vulnerable. He is often accompanied by the floating boy, who can also be temporarily stunned to prevent the Man on Fire's revival.
