A flare stack gas burner for waste combustible gas from oil refineries, chemical plants, oil production rigs, LPG and other marketing terminals, pipe lines and the like is disclosed which includes a stack with a centrally disposed combustible gas delivery pipe having a divider at the top with arms for upward delivery of the combustible waste gas through a plurality of radial slots to a mixing space, air under pressure being supplied to the stack and between the arms to the mixing space, a rotary diffuser being provided above the mixing space for directing the combustible gas-air mixture for combustion thereabove in a cylindrical or flaring frusto-conical vortex for smokeless combustion. Suitable gas pilots and igniters are employed. An optional flaring frusto-conical shield may be provided for a portion of the burning vortex where required.