I had the same issue with a Kindle Paperwhite where it would restart constantly. It would only allow me to open a book and as soon as I paged forward or backward it would restart. It would also restart/reboot when I attempted to select some of menu the settings. A couple of hard resets did not help and I could not get to the reset selection in the Settings menu before the Kindle would restart.
What finally worked was quite simple. I logged into my Amazon account on my computer and deregistered my device under "Manage Your Content and Devices". Your kindle should be connected to wi-fi for this to work. The kindle will then show up as Unregistered. I registered the Kindle again to my Amazon account and after that, the Kindle worked as it should - no restarting.