Fire could be a living thing and fire couldn't be a living thing, not every thing needs oxygen to be alive but needing oxygen doesn't mean you cannot live. When something oxidizes it releases heat, so fire is just really fast oxidization so fire is not alive when fire moves it is just air currents, fire is on Earth is a gravitational field so that is why it is thicker at the bottom. So the answer is no, fire isn't a living thing.
Hoped I helped:D