Hot gas is generally less dense than cool gas. A flame is very hot gas. Gravity pulls less on less-dense gas, so hot, less-dense wants to rise above cooler, denser gas. As the flame burns on earth, it takes the oxygen from the atmospheric air and and heats the surrounding atmospheric gases. So the hot air around the flame is pushed up as it is less dense And as the air around the flame is pushed up , the air around the flame is drawn towards the flame to take the space of the lighter gases that is pushed up. The colder air surrounding is pulled down by gravity. The flame is being pressurised all around by the atmospheric gases. This results in the flame being elongated upwards.
In space, where there is no gravity, a flame does not point upwards but will expand spherically around the source.