Amazon have updated the iOS version of the Kindle app fixing a registration issue that was causing problems with the last update. There have been various report that the last update was causing issues with device registration meaning users to have to re-download their books and loosing bookmarks.
Version 3.6.2 fixes the registration issues and have various bug and security fixes.
The app is free from the iTunes Store
What’s New in Version 3.6.2
• Fix for Registration Issue
• Various Bug Fixes and Security Fixes