You said "One Coil" was replaced. A twin cylinder has two coil packs. Each has a wire coming from it the attaches to the spark plug. The air gap between each and the flywheel is .10 thousands. You are correct in the white wire is usually the kill wire on a Kohler. I would suggest removing the sparks plugs attach one of the ignition wires for one of the plugs, clamp the plug to a metal surface with vise grips and spin the engine over with the starter. If you don't get a good spark the coils are bad or grounded. It is a very simple electronic circuit, the magnet in the flywheel moving across the two post on the coil generates a spark. Another thing to consider. When you replaced the flywheel did you get the key back in the keyway. If not the unit is out of time and will spark incorrectly at the spark plug.
If no spark when cranking with kill wire off and plugs out and .010 gap, than coil is bad. In 25 years of service I have never checked an electronic coil with an ohm meter. if the above is done that was the test. Only difference I have seen is when someone would install the coil upside down (usually on a Briggs).
This motor has one coil/ power pack that has dual magnetic pick ups. The air gap is correct and the key is in possion (this would throw the timing off but would still generate a spark out of time)
I'm annoyed because I am back to square one...Is it the coil or do I have another weak flywheel magnet. The new magnet feels just like the old one.
I think the magnet is probably fine.
One trick I use sometimes, I set the test up just before dark, and I do the actual test in the dark so I can see any stray sparks. Usually I don't have to resort to such measures, but I will routinely do this on a vehicle to assess the state of the wires and wire routing.
I started that as a kid...and dad's cars would put on a heck of a light show sometimes.