Wordpress - How to add post featured image to RSS item tag?

You could do it by adding an action to the hook 'rss2_item' like so:

add_action('rss2_item', function(){
  global $post;

  $output = '';
  $thumbnail_ID = get_post_thumbnail_id( $post->ID );
  $thumbnail = wp_get_attachment_image_src($thumbnail_ID, 'thumbnail');
  $output .= '<post-thumbnail>';
    $output .= '<url>'. $thumbnail[0] .'</url>';
    $output .= '<width>'. $thumbnail[1] .'</width>';
    $output .= '<height>'. $thumbnail[2] .'</height>';
    $output .= '</post-thumbnail>';

  echo $output;
});

Building off of codekipple's great answer, here's my modified implementation, which uses the valid Media RSS element media:content element (spec) and checking for the existence of a thumbnail/featured image:

    function dn_add_rss_image() {
        global $post;

        $output = '';
        if ( has_post_thumbnail( $post->ID ) ) {
            $thumbnail_ID = get_post_thumbnail_id( $post->ID );
            $thumbnail = wp_get_attachment_image_src( $thumbnail_ID, 'thumbnail' );

            $output .= '<media:content xmlns:media="http://search.yahoo.com/mrss/" medium="image" type="image/jpeg"';
            $output .= ' url="'. $thumbnail[0] .'"';
            $output .= ' width="'. $thumbnail[1] .'"';
            $output .= ' height="'. $thumbnail[2] .'"';
            $output .= ' />';
        }
        echo $output;
    }
    add_action( 'rss2_item', 'dn_add_rss_image' );

Note: Include the xmlns attribute here to make it validate. WordPress's initial install doesn't include that namespace declaration, and while you can change it, so can other themes/plugins.

More details on the other attributes etc. are in my non-WordPress-specific answer here.

This integrates with MailChimp's RSS newsletter building.