If your apps are not set to update automatically, you can manually update them at any time:
- Open the App Store app on your iPhone.
- Tap your profile icon in the top-right corner.
- On the Account screen, scroll down to see a list of pending updates.
- Swipe down from the top of the screen to refresh the list and check for new updates.
- Find the Kindle app in the list and tap Update next to it. Alternatively, tap Update All to download all pending updates simultaneously