The act of rolling a person on the ground to deal with flames is meant to extinguish them by cutting off the oxygen supply.
The correct word for putting out flames by depriving them of oxygen is "smother." This is exactly what happens when you roll a burning object or person on the ground.
Option (b) "kill" is inappropriate here because it refers to ending life, not extinguishing flames.
Option (c) "burn out" means something stops burning on its own after fuel is exhausted, which does not fit the immediate rescue action.
Option (d) "fizz out" means to end weakly or lose momentum, typically used for events or plans, not for extinguishing fire.
Therefore, "smother" is the most accurate and contextually correct choice.