A couple things to try...
- Are other apps able to toggle between landscape and portrait? If not then check to make sure you don’t have rotation lock enabled on your device.
- Restart your device.
- Uninstall and reinstall the Kindle app.
- If all else fails, wait for Amazon to patch to app. It might just be a compatibility bug with iOS 11.0.2. Knowing Amazon they’ll be quick to fix it.
The kindle app has a lock that you have to touch in order for it to change from portrait to landscape. It shows up on mine down in the lower right corner and once I touch it so the lock is "open" it will change to landscape mode.