Well if it is a carburetor fire or near the air inlet in general, opening the throttle could assist in "sucking" the fire out. If there is access fuel near the carburetor and burning, you would want the flames sucked through the engine.
Opening the throttle may also my help to "blow" a fire out.
On a radial engine that catches fire during start, normally due to over priming, the golden rule is to keep it turning. Do not halt the start process.