You may see the following message when opening an Office 2016 for Mac app:
This message is from Mac OS X indicating apps that use passwords require your permission to retrieve it from Keychain Access.
Click Always Allow in the message and you shouldn't be prompted for permissions again. Here's more detailed documentation from Apple on this message.
If you're repeatedly asked for the keychain, even after you click Always Allow, you may need to reset it. Follow the steps in this Apple support article to reset your keychain in Mac OS X.
Note: All Office 2016 for Mac apps share the same Keychain Access information, which means you just have to sign in and activate one app and the other apps will be automatically activated.