Using the @shanebp ideas of using get_comments
:
$args = array(
'post_author' => get_current_user_id(), // It will use the current logged in use to grab the comments
);
$comments = get_comments( $args );
// Referer to http://codex.wordpress.org/Function_Reference/wp_list_comments
$list_args = array(
'reverse_top_level' => false // Show the latest comments at the top of the list
);
wp_list_comments( $list_args, $comments );
This will display the list of comments done on posts from one user.