Here is how to show taxonomy terms in rss feed. Just add this to the functions.php file and update the $tax and $post_type variables to match your needs.:
add_filter('the_category_rss', 'wpq_the_category_rss');
add_filter('rss2_ns', 'wpq_rss2_ns');
function wpq_the_category_rss($the_list_original)
{
$tax = 'announcement_tags';
$post_type="announcements";
if(get_post_type() != $post_type)
return $the_list;
$categories = get_the_terms(get_the_ID(), $tax);
$the_list="";
$cat_names = array();
if(!empty($categories))
{
foreach((array)$categories as $category)
{
$cat_names[] = sanitize_term_field('name', $category->name, $category->term_id, $tax, 'rss');
$cat_descriptions[] = sanitize_term_field('description', $category->description, $category->term_id, $tax, 'rss');
}
}
$cat_names = array_unique($cat_names);
$cat_descriptions = array_unique($cat_descriptions);
foreach($cat_names as $cat_name)
{
$the_list .= "\t\t<category domain=\"". $tax ."\"><![CDATA[" . @html_entity_decode($cat_name, ENT_COMPAT, get_option('blog_charset') ) . "]]></category>\n";
}
foreach($cat_descriptions as $cat_description)
{
$the_list .= "\t\t<wpq:category_description domain=\"". $tax ."\"><![CDATA[". @html_entity_decode($cat_description, ENT_COMPAT, get_option('blog_charset')) ."]]></wpq:category_description>\n";
}
return $the_list_original.$the_list;
}