Please see the “Getting values from other places” on this page https://www.advancedcustomfields.com/resources/get_field/. You need to supply the correct $post_id value that matches the category.
$categories = get_the_terms( $post->ID, 'domain_type' );
foreach( $categories as $category ) {
$icon = get_field('domain_icon', $term->taxonomy.'_'.$term->term_id);
echo '<i class="fa'.$icon.'"></i>' ;
}