When I open IOS Outlook app, it appears to open but then I'm kicked out immediately back to app library screen.

Hello koppei,

If an app on your iPhone or iPad doesn't work as expected, we recommend following the steps here: If an app on your iPhone or iPad stops responding, closes unexpectedly, or won’t open

You can find more information in the article above, but here's an overview of those steps:

1. Close and reopen the app

2. Restart your device

3. Check for updates

4. Delete the app, then redownload it

If you need more help and you found the app on the App Store, contact the app developer. 

Thanks.