Redirect current user to their most recent custom post

To get the permalink of a users most recent post (of custom post type) perform the following query:

$latest = get_posts(array(
        'author' => $current_user->ID,
        'orderby' => 'date',
        'post_type' => 'my_custom_post_type',
        'order' => 'desc',
        'numberposts' => 1,
    ));
    if( $latest ) {
      $url = get_permalink($latest[0]->ID);
    } else {
      // No posts
    } 

For the redirect part take a look at the function wp_redirect.