I just installed a kohler toilet fresh from the crate. The fill valve runs every few seconds for just a few seconds. I suspect a leak but can't find any water drops in or around the toilet. Can you help?

Either...
Low water pressure.
The inlet valve isn't opening fully.
Small bore pipework.

Is the water pressure good in the rest of the property?
Is so then there may be an isolation valve on the toilet which isn't fully open.

There is a rubber seal at the bottom of the flush valve that covers the openning at the bottom of the tank. If this rubber seal has perished slightly then it will leak water into the toilet bowl. This rubber seal need to be replaced to form a proper seal to prevent water leak.

you can't just replace 1 part in a toilet, your flapper is worn and needs replaced as well.

Try replacing the rubber flapper inside the tank.

There is a screen @ the inlet to the vavle where the water connects that may be plugged or contact Kohler they will send you a repair kit for the fill valve.

The Kohler Cimarron is one of the most popular and reliable toilets out there. (My Favorite). However, depending on the hardness of the water and if you use cleaner tabs in the tank, these factors can lead to a malfunction.
The first thing you should do is hold the flapper (rubber seal inside the tank that releases the water down to the bowl) down with your hands for a few seconds after a flush and see if the toilet stops running. Sometimes the flapper doesn't seal properly therefore the fill valve keeps working non stop. Stopping the fill while holding the flapper down will confirm that your flapper needs to be changed.
If this doesn't work then try this....
The other common problem with a running toilet is with the fill valve itself. There is an attached float on the fill valve that goes up and down depending on the water level. Once the water level rises, it rises the float, and the float tells the fill valve to stop filling the tank. While the toilet is running (hissing), try raising the float all the way up with your hand and see if it stops. If it stops but not consistently with every attempt, then you will need to change the fill valve. I believe the Fluidmaster 400A is the replacement model.

check fill tube from the fill valve to the flush valve, if the end of the hose is close to the watr level it will back syphon.... recommend also putting in better inner components.. fluild master 400 a fill valve and a nice red korky flapper

There is a volume control screw on the valves usually a plastic thumbscrew on side of valve turn clockwise until they quiet up the plumber should have adjusted that these are very tempermental toilets but when adjusted properly are excellent toilets I have 2 in my own home

I had exactly the same problem. Just turn down the water pressure @ the valve on the water inlet line. While you have the toilet lid off, you may want to remove the fill valve (1/2 turn counterclockwise on the plastic nut attached to the water-in line), and clean the rubber diaphrams (there are 2). They will sometimes get gritty and this will cause some fill noises and leaking.

Sounds like your flapper is leaking causing the water in the tank to lower until it triggers the fill valve. Replace the flapper (they're cheap and wear out easily).