You cannot extinguish NetNavi Net's flames in Mega Man 3 (Game Boy / Mega Man III / Rockman World 3). They are an attack pattern, not an environmental hazard.
Game Boy Mega Man III (1992) condenses NES Mega Man 3 Robot Masters. Net (from Mega Man Battle Network) does not appear. If you mean Fire Man / Heat Man / Burner Man stages, the same evasion principles apply.
Quick reflexes and smart weapon choice win the day.