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. 

Admin 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.

User settings:

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

Extensions:

Read on how to configure the available here: