Just want to add:
(I am assuming this Kohler has battery/coil ignition.)
Do you have a volt/ohm meter? If you do, check for 12v or near 12v. on the coil (+) positive terminal. If you have 12v. there, problem is on engine. If no 12v. on that terminal, your issue is in the wiring on the mower chassis.
If the problem is on the engine, check for voltage on the wire to the points, at the terminal screw on the points. When the points are open, there should be some voltage there, but probably not 12 volts. If the points are closed, you may not see any or very low voltage there, so roll the engine over until the points open and check again.
If you have voltage to the points, try filing the points, or replace the points, like someone else suggested. Point gap should be about .018 or .019, sometimes less. (Point gap will change some if timing is adjusted to spec.) If you have no voltage at the points, try a different wire between the coil (-) and the points. I have seen that wire short through the insulation and kill the spark, sometimes intermittently.
Some other thoughts if still no spark: I have seen points grounded to point cover on those covers with the grounding plunger in the cover. I have also seen engines have problems firing with a resistor sparkplug wire. You can substitute a piece of stiff sold copper residential wire temporarily for a sparplug wire, just bend it so it is about 1 inch from anything it can ground to. Try another known-to-be-good coil. Try another known-to-be-good condenser.
Hope this helps.
hope this helps. If