My immediate assumption was that the ground wire between the bridge of your guitar and the back of one of the pots was faulty. However, when I thought about it that would more likely mean that the noise reduced when you touched the strings as you would become the ground. Did I interpret the original post correctly. The noise isn't there when you don't touch the strings but APPEARS when you do touch them?
You said that you have ruled out the guitar but have you checked for a faulty cable between guitar and amp. Sounds possible that you have poor screening in the cable itself.
You are right to try and get to the root of the problem. Covering this kind of thing with a noise gate is never a good solution. The noise gate is usually best as an effect (to create super tight muting) or to reduce excessive hiss from very high gain sounds. Your Kemper shouldn't make this kind of noise so there must be something causing it. The only question is what? Unfortunately that can sometimes take a lot of time and effort to figure out so many people just resort to the noise gate instead of fixing the real problem.