Well, you either have a hardware fault or software corruption. As you have already tried wiping the user area and updating the firmware, a hardware fault seems more likely as suggested by the poster above.
You can try charging your device with a wall charger for a minimum of 24 hours (slow charge curve for a possibly failing battery). And you could try waiting it out a few days in case the system is doing extended error checking to try and recover. A process can literally take days to complete.
Other than that, about all that is left is perhaps considering a serial port adapter (which would need to be soldered to your Kindle internally) which would provide a kernel log. This would probably confirm the nature of the errors.
Odds are though that it's the eMMC (flash memory) problem described above which is not practical to repair. ./
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