Smoke rises due to convection current. The solid particles emitted from a combustion process are carried by the hot air that rises because of its lower density than the surrounding air. The horizontal motion of smoke itself is affected by the movement of air surrounding it.
Flat-Earthers claim that a rising smoke without horizontal motion “proves” a stationary Earth. They are wrong. The horizontal motion of smoke is an effect of the horizontal motion of air relative to the smoke, and the motion of the object emitting the smoke is inconsequential.