As seen on the https://clicknathan.com blog:
How to Allow Subscribers to Delete Posts from the Front End while Still Blocking the Admin Area
Allow WordPress Authors to Delete their Posts from the Front End

Additionally, here is a simple script to put within the loop to display a delete link for anyone with the rights to edit posts:

$url = get_bloginfo('url');
  if (current_user_can('edit_post', $post->ID)){
    echo '<a class="delete-post" href="'; echo wp_nonce_url("$url/wp-admin/post.php?action=trash&post=$id", 'delete-post_' . $post->ID);
    echo '">Delete post</a>';
  }