Flight Instructor reported after an initial a temp to start a C152 the instructor decided to let the starter cool. Two minutes later; flames were seen coming from the air inlets and dripping near the nose gear.

Narrative

When I arrived to ZZZ I pushed the airplane out of the spot and moved all my things in to the plane to prepare to fly back to ZZZ1. The preflight had no issues; apart from the cowling fuel sump drain was expelling more gas than on other C152s. Seeing as I had never flown the plane before; I didn't consider it to be anything of concern. I ensured it was not still open or leaking and prepared to leave. Once finishing preflight I followed the checklist and attempted to start the airplane with the ignition switch. I cranked it about 3-4 seconds and then turned everything off to give the starter a quick rest. I realized I hadn't put the mixture to full rich on the first attempt; so I redid the starting checklist again and primed the engine (maybe once or twice; I can't remember) and began cranking the ignition switch. With no success after about 5 seconds; I didn't want to crank too long so I decided to give the starter a break. I stepped out of the airplane about 20 yards away after ensuring the mixture; master and ignition switches were off. After about 2 minutes I looked back and saw smoke coming from the cowling. As I approached the airplane I saw flames coming from the air inlets and dripping near the nose gear. I immediately double checked the mixture; master; switches; and ignition were all off and grabbed the fire extinguisher from behind the seat. I attempted to extinguish the flames; but it was not enough. Two men came with larger fire extinguishers and yelled 'is the fuel shutoff off?' (which I had forgotten). I quickly opened the door and shut off the fuel shutoff switch. Then the two other guys were able to extinguish the fire. A cop arrived to see what was going on and then 5 minutes later the fire department from ZZZ arrived. The fire never reignited after initially being extinguished.