Urls in Custom Post Type work for Terms but not for its Taxonomies

[taxonomy_name] should be available in permalink automatically if you register it as

register_taxonomy('kalendar', [taxonomy_name], $args );

So Try this

foreach($this->months as $month => $month_var) :
  $args = array(
    'labels' => array('name' => $month),
    'hierarchical' => true,
    'rewrite'      => array( 'slug' => $month_var ),
    'query_var' => true
  );
  register_taxonomy($month_var, 'kalendar', $args);       
endforeach;

Then Save Permalink Settings to flush rewrite rules.

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