The add-on is based on the 'Page Search' dashboard page. Therefore some functionality has been copied and modified. It's not possible to do bulk actions like 'permissions', 'move' or 'delete'. This is because a stripped version of the plugin is -in my opinion- better for future stability.
The plugin checks for the 'canEditPageSpeedSettings' permission when the actual flushing starts. This means that if one has selected pages without having those permissions, clearing the cache won't work for those pages.
After clearing the cache a message pops up how many pages have been affected.