Just purchased my first K22. It needed a good cleaning. The cylinder flutes are a gray color. I have seen this on larger calibers and it was carbon that cleaned right off. None of the gun cleaning solvents have had any effect. Looking for any information or ideas. Thanks for reading.

Soaking is your friend.
If bore solvents don't do it fast enough, use a gun safe carbon remover.

The worst carbon problem I ever had was the gas cylinder and muzzle brake on my AK-74.
I tried everything........ packing them with paper towel and soaking with bore solvent, using a lead away cloth, and Slip 2000 Carbon Killer, nothing worked.

Then just as an experiment I used Shooter's Choice Extra Copper solvent and the paper towel packing.
To my surprise the carbon was removed down to the hard chrome plating.

Old Hoppes works very well IF you have any.