Hello Richard,
The component displayed here is a {{flagged-post}} if I’m not mistaken. If you open adminjs/templates/components/flagged-post.hbs you will see {{plugin-outlet name="flagged-post-controls"... and {{plugin-outlet name="flagged-post-below-controls"...
This is where you want to hook your plugin. If you don’t know about plugin-outlet yet, I recommend your read Beginner's Guide to Creating Discourse Plugins Part 2: Plugin Outlets
Hope it will be helpfull.