Adding a function as a new item

Try that code. Please append it in the functions.php of the theme:

// Passed parameter: an array of social media icons as list items
function kalawebs_add_flags_in_bar ( $list_items ) {

    // Add flag list as last item in the list, via $array[]
    // The content has to be surrounded by the LI element
    $list_items[] = '<li>^' . cml_show_flags( array( 'echo' => false ) ) . '</li>';

    // Returns changed list
    return $list_items;

}

// Let the function work
add_filter( 'speed_contact_bar_icons', 'kalawebs_add_flags_in_bar' );

That will print out a UL list with the flags. If you want to style the UL you can use CSS.