As of version, 5.0 Inbox for Jira supports extensions.

Extensions

All extensions are available for download from the Atlassian Marketplace: https://marketplace.atlassian.com/vendors/1214651/rixter-a

To install an extension you need to have the Inbox for Jira pre-installed in your Jira instance

Configure extensions

Once an extension is installed its configuration interface will appear below the standard Inbox For Jira settings.

Go to the apps settings page

Click the Inbox for Jira settings in the menu on the left-hand side

Scroll to the bottom of the page to find the extension settings.

Click the cogwheel on the right-hand side at the bottom of the notifications panel

Read on how to configure the available here: