Your best bet may be to do a Factory Reset. This is Settings -> Device -> Reset to Factory Defaults. This wipes out all your files (all ebooks, all apps, etcetera) and also the Fire's registration to your account. So if you do this you have to reenter your WiFi password, and then reregister your Fire. So this is a drastic step, but I think your Fire's Books database is likely corrupted and there may be no alternative.
If you want to try less drastic steps first, I would start with a hard reset by holding the power button for 20 seconds. If that does not help, clear the Books cache from Settings -> Apps -> All Apps -> Amazon Kindle -> Clear Cache. If that does not help try "Clear Data" from the same page (I'm not sure if this deletes the ebooks or just their entries in the Books app). If none of this helps, then go for the Factory Reset.
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