If the update screen is blocking everything, your best option is probably to free up enough storage so the update can complete. If that's not possible, check the Kindle jailbreak community to see if anyone has found a workaround for that specific firmware version before attempting anything risky. I had a similar issue with another device, and sometimes completing the required update is the only way forward. Once everything is working again, I usually switch back to reading manga with
Tachiyomi APK on my Android device.