There is a way to rollback the update. Install Kindle from the Amazon app store which still has version 4.13
1. Uninstall 4.14 from your device.
2. Reboot your device.
3. Install Amazon Appstore for Android on your device. It is found on
http://amazon.com. Follow the instructions to run the install.
4. Open the Amazon Appstore on your device and search for the Kindle app. Verify that it is still version 4.13.
5. Download and install the Kindle app. Continue the setup process to connect to your account after you open the app.
I was able to rollback to the previous version and now my Asus tablet is working again. I'd recommend doing this sooner than later as I don't know how long the older version will be there.
Good Luck