I have a Kohler K-10416
Welcome to fixya!
Is the low water flow in both hot and cold? If it is only one that has a reduced flow, then check the incoming water lines under the sink for any kinks in the hose. When you took off the aerator, did the water flow increase without the aerator on? If it did, then soak the aerator in a vinegar/water solution for a while to clear the buildup from the screen. I know you said you cleaned the screen out, but sometimes a film will build on the screen also.
If the reduced flow is from both, probably the valve needs to be replaced. Be sure to turn the water off at both hot and cold before disassembling your faucet.
There are some things you can check once you disassemble the faucet. An o-ring could have disintegrated and plugged up the flow, or maybe it's out of place. Or, you could have crud buildup inside the valve. Once you get the valve out, you can try flushing it out by soaking it in a vinegar/water solution and then replacing it. If that does not help, then replace the valve. You must have the exact valve number as different model faucets use different valves even from the same company.
Here is a webpage with a parts diagram for your faucet: http://www.us.kohler.com/onlinecatalog/pdf/1084452_2.pdf
Page 8 has directions on how to get to the valve.
Hope this helps. If it does, I'd appreciate your vote. Thanks,
on Jun 29, 2011