$args = array('fields'=>'all');
$terms = wp_get_post_terms( $post->ID, 'customtaxonomy', $args );

foreach ($terms as $category) {
  $cat_id = $category->term_id;
  $post_id = 'customtaxonomy_'.$cat_id;
  $value = get_field ( "example", $post_id );
}