I've tried cloning a private repo (that I have access to) on GitHub and get this message:
Clone Failed
Could not connect to 'origin'. Double-check your remote url, then make sure you have access to do that action on that remote and try again.
I run Windows 10, I have connected Kraken to GitHub and ssh key works and I can push and pull repos to my other GitHub repos that are public just fine. I was also able to clone the repo from the command line just fine.