Outlook 2016 Mac change order of accounts
I wanted to know the same thing.  I searched and couldn't find an answer.  I finally figured it out myself.  You can change the "default" account and it will go to the top.  Go to Tools, Account and then select the account you want to be the default.  Click the gear at the bottom and select "Set as default."

Then, the remaining accounts will be put in alphabetical order.  You may need to exit Outlook and reopen it to see the new order.

This works better than deleting the top account - letting the items shuffle and then adding the other accounts below since the sort order doesn't always follow the order of addition to the app. Especially if you have delegate accounts you're adding.