If you have a flooded carburettor fire during start (which I was right seat for once) keep cranking, get it running, and pull the fire through the engine, where it will do the least harm. Once the engine has run for a minute, shut it down, and have the induction inspected for possible damage.
A fire in flight will not be an induction fire, as the engine is running. In the case of any fire, remove the fuel, then oxygen, and heat, if possible. In the case of an engine fire in a 172 in flight, you only have control of fuel, so turn it off (mixture and fuel selector). There is only a small amount of fuel available to burn forward of the fuel selector, so don't worry about that. You're headed down then, so just focus on a good forced landing, there's little to burn dangerously up front, if the fuel has been turned off.