how to flush custom author rewrite rule

So, I’ve created custom AUTHOR url like

domain.tld/user-nicename, and i have now links like domain.tld/john-doe.

My functions.php is

// AUTHOR
add_filter('author_rewrite_rules', 'no_author_base_rewrite_rules');
function no_author_base_rewrite_rules( $author_rewrite ) {
    global $wpdb;
    $author_rewrite = array();
    $authors = $wpdb->get_results("SELECT user_nicename AS nicename from    $wpdb->users");
    foreach($authors as $author) {
        $author_rewrite["({$author->nicename})/?$"] = 'index.php?    author_name=$matches[1]';
    }
    return $author_rewrite;
}

if( !is_admin() ) {
    add_action('init', 'author_rewrite_so_22115103');
}

function author_rewrite_so_22115103() {
    global $wp_rewrite;
    if( 'author' == $wp_rewrite->author_base ) $wp_rewrite->author_base =     null;
}

I am creating users programatically with wp_inser_user, where i set all needed info.

But when I approach domaon.tld/new-user, i’ve got 404 NOT FOUND, until I’ve re-save permalinks.

SO the question is, how can I exactly set this re-saving of permalinks programmaticaly after each use

Just use flush_rewrite_rules(); Documentation here.