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That is a SCAM message. It is also called ransomware and it has been around for a few years. Don't pay the ransom.
First soft-reset the Kindle. Press and hold down (or slide) the Power button for 20 seconds and this will reset the Kindle. Now we can clear the browser/silk app. Follow the steps below;
1. Tap the Settings icon from the Home screen and select "More" (or swipe down from top and select Settings)
2. Tap "Applications" and select All Applications.
3. Find and select the Silk or Web/browser app. Then tap Clear Data and Clear Cache. Restart your Kindle.
If that didn't work, then we have to boot your Kindle to Safe Mode and factory reset the device. Turn off Kindle. Then press and hold down Volume Down and Power button at the same time for a few seconds and this will boot into Safe Mode.
After booting into Safe Mode, Go to Settings. Tap Device Options, and then tap Reset to Factory Defaults. Tap Reset to confirm. Resetting to factory defaults will erase everything from your Kindle. But after factory reset, you can re-register it with your Amazon account you used on it to redownload all your books/contents without paying again.
Please let me know if that didn't work, so we can continue troubleshooting.
Remember, this is not my final answer. If my solutions didn't work please don't rate me bad or poor. Instead please reply back to me and I will continue to help you until we fix the problem or you are satisfied.