Native gallery custom html output

Is this what your looking for, here? get_post_gallery_images().

This is the example for that page.

add_filter( 'the_content', 'wpdocs_show_gallery_image_urls' );

/**
* Show image URLs below the content
*/
function wpdocs_show_gallery_image_urls( $content ) {

    global $post;

    // Only do this on singular items
    if( ! is_singular() )
        return $content;

    // Make sure the post has a gallery in it
    if( ! has_shortcode( $post->post_content, 'gallery' ) )
        return $content;

    // Retrieve the first gallery in the post
    $gallery = get_post_gallery_images( $post );
    $image_list="<ul>";

    // Loop through each image in each gallery
    foreach( $gallery as $image_url ) {
        $image_list .= '<li>' . '<img src="' . $image_url . '">' . '</li>';
    }
    $image_list .= '</ul>';

    // Append our image list to the content of our post
    $content .= $image_list;

    return $content;
}