You can add your flag (plain) html into menu at last li tag.
<?php
function add_last_nav_item($items, $args) {
if ($args->menu->slug == 'topbar-menu') { // change your menu slug name
// Add your html
$item = '<li class="searchbox">
<input type="search" placeholder="Search......" name="search" class="searchbox-input" onkeyup="buttonUp();" required>
<input type="submit" class="searchbox-submit" value="">
<span class="searchbox-icon"><i class="fa fa-search"></i></span>
</li>';
$items = $item.$items;
}
return $items;
}
add_filter( 'wp_nav_menu_items', 'add_last_nav_item', 10, 2 );
?>