Show custom field from custom taxanomy term on custom post type

Use the get_the_terms function instead so you can build the list manually and access the term_id for each term.

$terms = get_the_terms( $post->ID, 'taxanomy-name' );
echo '<ul>';
foreach( $terms as $term ):
    echo '<li>';
    echo $term->name;
    the_field( 'custom-field-name', 'taxanomy-name_' . $term->term_id );
    echo '</li>';
endforeach;
echo '</ul>';