Had the same issue. Frustrating! And no help anywhere.
Have an Android Phone and Office 365.
Uninstalled all Office 365 Apps and re-installed, rebooted phone many times. Tried adding new Accounts in Phone settings. Then, when adding an Office 365 account to Android, got a message "have to do it via one of the Microsoft apps on the phone". (Obviously
not the Outlook App as we experienced.) So, tried Word, and was able to add Office 365 Account via Word. But then got an actual helpful error! It said to update the app on my phone called "Android System Web View App". And gave a link to update it. So, updated
this app, again rebooted the phone, and then went back to setting up Word with Office 365 again (basically, signing into Office 365 via Word). Once I was in Office 365 on Word, I opened Outlook. Voila, all my emails are there and syncing.
Another thing to note is that before all this resolved I was seeing a syncing error in Outlook account (Phone settings - Accounts). It said "Sync is currently experiencing problems. It will be back shortly." Unfortunately, that error is still there, but
email is synced and up to date. So, hopefully that fixes itself.
What a mess! Wish Microsoft provided better support for all this for sure! Especially when you pay a monthly fee for Office 365!