Update: The new update to 3.6.2 is out and is safe. If you updated to 3.6.2 and did not open the app, updating to 3.6.2 and then opening the app is safe. (At least it was safe for me.)
Lilliputing and a few other sites are reporting that Amazon has said to not upgrade the current 3.6.1 Kindle app on iOS.
The update will wipe all books and settings from your device and force you to re-download your books and re-register your device.