I've run into two issues while trying to use this plugin in a multi site environment:
1) The path to admin-ajax.php is incorrect for wp installations in subdirectories. Changing $current_blog->siteurl to $current_blog->path (around line 91) solved the issue.
2) The cookies used to remember which comments a user have flagged only include comment_id, not blog_id, so if comment 1 on blog 1 is flagged, the user can't flag comment 1 on blog 2. This is solved by adding the blog_id to key in the cookie, ie $data[ "$blog_id-$comment_id" ] instead of $data[ $comment_id ], in methods already_flagged and mark_flagged.
Hope this can help anyone, contact me if you need the actual code.