Call 1-800-4-KOHLER and you can tell them that you bought one of their (Expensive Junk) faucets and now you can't find it even on their website to get parts... (so typical for Kohler)
Tell them it looks a lot like the K-12185 Fairfax(R) single-control remote valve kitchen sink faucet with sidespray and lever handle
then explain the differences.
You should be able to get free parts under their lifetime guarantee but it may take a month or, so (again typical for Kohler) to get them...
Why do I hate Kohler?
Because every fixture they make they reinvent the wheel sometimes several times on the same part number so finding the parts is a nightmare and they have so many parts they don't even stock them at the factory.... Just my