$parent_tag_id=397; // your tag id here
JLoader::register('TagsHelperRoute', JPATH_BASE . '/components/com_tags/helpers/route.php');
$tags_tree=JTable::getInstance('Tag', 'TagsTable')->getTree($parent_tag_id);
// Show children:
foreach($tags_tree as $tags_tree_id=>$tags_tree_item) {
echo 'DEBUG: ';
echo ' id:' . $tags_tree_item->id;
echo ' level:' . $tags_tree_item->level;
echo ' path:' . $tags_tree_item->path;
$link=TagsHelperRoute::getTagRoute($tags_tree_item->id . ':' . $tags_tree_item->path);
echo ' link: ' . JRoute::_( $link, true, 1);
echo '<br>';
}