Hi Johnny2spades,
Welcome to Apple Support Communities. We understand that you're having an issue with opening the Kindle app on your iPad mini and iPad Air 4th generation. We'd like to help you get this working again.
Have you tried to force the Kindle app to close and then reopen it? If not, that's a great first step to see if the app will successfully load after that: Close an app on your iPad
If that doesn't resolve it, you can try to Restart your iPad. Does that help the Kindle app to load? If not, check to see if there is any updates available since you last updated. You can check both the iOS update and the app updates.
Then, if it still won't open on one or both of your iPads, removing the Kindle app and resintalling it can help:
How to delete apps on your iPhone, iPad, and iPod touch
Redownload apps and games from Apple
Finally, if you continue to have issues with this specific app, reaching out to the app developer may help you get this resolved.
How to contact an app developer
Hope that helps!