How can I clear the Menu cache after saving some configuration?
Your form code would be helpful to see here to determine if you are using a system_settings_form() function (which seems likely since you are creating a module configuration form) or just a simple form. Regardless, the answer for both is to add a submit_handler to your form.

Basic Form with Submit Handler: https://www.drupal.org/node/717740

If you are not using system_settings_form, than you can add your post-submit actions to a function named after your form definition function, or 

/**
 * Add a submit handler/function to the form.
 */
function my_form_submit($form, &amp;$form_state) {
  &lt;YOUR menu_rebuild STUFF HERE&gt;
}


and Form API will automatically find it. If you are using system_settings_form() for your admin form, than you can add your submit handler by adding this before calling system_settings_form()

$form['#submit'][] = 'my_form_submit';