Welcome to MLMF!
For starters, what model is your Kohler?
When it comes to fuel, it could be a number of possibilities. I'd check the fuel filter first to make sure it's not clogged and that its getting fuel through it. It's been known to happen. If it's ok, I would venture to the carb as it probably has an obstruction somewhere in it. To clean it, you can pull it apart and soak it or blow compressed air through the ports. If it is later unit and has a fuel pump, the problem could lie somewhere related to that like a faulty/corroted connection somewhere.
Spark wise if it has a points and condenser type igntion, I'd clean and check the point gap. If a no go, I'd venture onto the condenser. If the ignition is electronic I'd probably have the ignition coil tested and check all the connections to make sure they are clean.
Here are some links to visit: