I saw (with gratitude) a CCleaner app for Kindle Fire. But after running it, finding lots of stuff, the "clean" button was grayed out.
I, too, wanted to use CC Cleaner on my Kindle Fire 10. It will analyze but the clean button is disabled. The Amazon tech - who worked to get the program operational, finally said (sigh) it is a developers problem and not a Kindle/Amazon one. I have used this program for years on my PC and now this little pipsqueek of a computer comes along and can't handle the app.
So is this the greyed out button (in my image)
Have you given ccleaner storage permission? What android version?