Passing arguments to my function with do_action and add_action is not working

You are doing the do_action before the action is add, try moving it:

$name = "link";
add_shortcode($name, 'aa_link_shortcode');

function shorcode_resources($var1) {
    global $post;
    $shortcode_found = false;

    if (has_shortcode($post->post_content, $var1)) {
        $shortcode_found = true;
    }

    if ($shortcode_found) {
        wp_enqueue_style('core', ABS_URL . '/shortcode/css/flipbox.css', false);
        wp_enqueue_script('my-js', ABS_URL . '/shortcode/js/flipbox(' . $var1 . ').js', false);
    }
}

//first we add the action
add_action('wp_enqueue_scripts', 'shorcode_resources', 10, 1);
//then we do the action
do_action('wp_enqueue_scripts', $name);

also remember that wp_enqueue_scripts its an action that WP will trigger too