The bolts that hold the tank on must only have a rubber washer IN the tank. The metal washer must go outside the tank. If you have a metal washer in the tank, that may be causing the leak. Also, it is best if you actually use four nuts and metal washers. The first one directly on the bottom of the tank to seal it up well, then, the second one to attach it to the bowl. Most toilets have enough room for that second nut and washer, but knowing Kohler, maybe not!
Generally, you can tighten the tank bolts up until the tank is sitting on it's spacing legs (but, your Kohler may not have any!) IF you tighten them slowly, and a little bit, alternating side to side.
Your toilet may have been specifically designed for that big gasket, and may not work well with a generic rebuild kit. Can't say without seeing it - Kohler has a tendency to do things their own way, and generic is distasteful to them.