From Kohler CH 11 - 16 Service Manual
Engine Cranks But Will Not Start
1. Empty fuel tank.
2. Fuel shut-off valve closed.
3. Dirt or water in the fuel system.
4. Clogged fuel line.
5. Spark plug lead disconnected.
6. Key switch or kill switch in off position.
7. Faulty spark plug.
8. Faulty ignition module.
9. Choke not closing.
10. Faulty oil sending unit.http://www.kohlerengines.com/manuals/landing.htm
Section 8 is the electrical wiring diagram for the engine.
One other problem I had with the Kohler Command series is a wire coming unpluged on the back of the switch.
If all else fails, check the flywheel key. Make sure it's the correct size. Briggs and Stratton