Hi, so the “Report Phishing” button is an Office Add-in that can be deployed to your users through the Microsoft 365 admin center. The deployment options available depend on the Office application you’re targeting and the type of add-in you create.
For Outlook, you can deploy add-ins using the Exchange server for both on-premises or online environments. This means that it should be possible to deploy the “Report Phishing” button to users running Outlook/Office 2016 as well as those on Office 365.