Question

why the fire always moves in the upward direction?

Answer 1

Because the products of the fire are hot gases, and their heat makes them much less dense, and hence much more bouyant, than the air around them. (The reduction of gas density with increasing temperature is reflected in the ideal gas equation of state, if you've studied that. Otherwise, you can understand it as the result of high temperature representing an acceleration of the motion of gas molecules -- and the faster they go, the harder they push against any confinement, so the gas gets less dense.)