WARNING 1: I do not know if this looses your book progress or downloaded books. I had a freshly rooted kindle with no books downloaded. But your cloud does work. It will bring up books you have purchased.
WARNING 2: You will no longer be able to use the books tab in original Kindle Launcher. ( always backup any system app that is removed before removing it by copying and pasting it somewhere safe )
1. Remove old kindle app: Go to your file explorer of choice and go to your /system/app/ folder and cut the Kindle for Otter apk and paste it in /sdcard/download/ folder for backup.
2. Reset kindle now you have no kindle reading app once reset is complete.
3. Now download new version from here http://db.tt/G14HspkX and install it.
4. Now go back to your file explorer and in your sdcard folder there should be 2 folders for the kindle app Books and Kindle. Open the books folder And copy all the files and folders in the books folder to the kindle folder. Then delete Books folder.
5. Reset kindle and when restart is complete you should have the kindle app working in your launcher.
If someone with books downloaded and progress made on their books could please post if this transfers your info to the new app this would be great.
Please give thanks to those who help. Everyone here helps and devotes there time to each other. Especially the developers. A thanks goes along way and is much appreciated.
EDIT: This does not work with the kinology rom.
Sent From My Rooted Kindle HD 7"