How to add image for custom taxonomy

You can use get_object_taxonomies() as your solution.

Returns all the taxonomies for a post type or post object:

<?php get_object_taxonomies( $object, $output ); ?>

Have you tried anything? something like this?

// taxonomy term archives
$post_type = get_post_type(); // find out if CPT
$taxonomies = get_object_taxonomies($post_type); // Find taxonomies
if($taxonomies){
    foreach($taxonomies as $taxonomy){
        // only want hierarchial -- no tags please
        if(is_taxonomy_hierarchical($taxonomy)){

            $terms = get_terms($taxonomy); // find out "terms" e.g. catoegries, for each taxonomy

            foreach ( $terms as $term ) {  ?>
                $term_link = get_term_link($term->slug, $taxonomy);
                $term_name = $term->name;

                //Image section like below...
                if (function_exists('z_taxonomy_image_url')) { ?>

                    <img class="category-thumbnail" src="https://wordpress.stackexchange.com/questions/196673/<?php if (function_exists("z_taxonomy_image_url')) echo z_taxonomy_image_url(); ?>" alt="<?php the_title(); ?>" title="<?php the_title(); ?>"/>
                <?php } 
            }
        }
    }
}

This how you can get taxonomy with image.

The Categories Images Plugin(https://wordpress.org/plugins/categories-images/) allow you to add image with category or taxonomy.