How to add toggle-able DOM element after nav menu item?

You can easily add any HTML element to all menu items that have children by extending the Walker_Nav_Menu core class. The code below will add <i> icon element just after menu item </a> tag but you can of course change that if you need them inside or somewhere else by changing the $item_output variable.

function yourprefix_menu_arrow($item_output, $item, $depth, $args) {
    if (in_array('menu-item-has-children', $item->classes)) {
        $arrow = '<i class="fa fa-angle-down"></i>'; // Change the class to your font icon
        $item_output = str_replace('</a>', '</a>'. $arrow .'', $item_output);
    }
    return $item_output;
}
add_filter('walker_nav_menu_start_el', 'yourprefix_menu_arrow', 10, 4);

Cheers!