MyHome Language Switcher was designed to work only with WPML Plugin. However if you wish to customize it other way you can use this article. 

1. Language switcher is located in the /wp-content/themes/myhome/header.php file

2. Please backup the file for security reason

3. Find Language Switcher Code in this file:

if ( My_Home_Theme()->layout->show_language_switcher() ) : ?>
   <div class="mh-wpml-top-bar">
      <?php foreach ( My_Home_Theme()->layout->get_language_flags() as $myhome_lang ) : ?>
         <?php if ( ! empty( $myhome_lang['url'] ) ) : ?>
            <div class="mh-wpml-top-bar__item
                                      <?php if ( ! empty( $myhome_lang['active'] ) && $myhome_lang['active'] == '1' ) : ?>
                                          mh-active-lang
                                      <?php endif; ?>
                                  ">
               <a href="<?php echo esc_url( $myhome_lang['url'] ); ?>">
                  <img src="<?php echo esc_attr( $myhome_lang['country_flag_url'] ); ?>" alt="">
               </a>
            </div>
         <?php endif; ?>
      <?php endforeach; ?>
   </div>
<?php endif; ?>

4. Change all above code lines into this new code:

<div class="mh-wpml-top-bar">
    <div class="mh-wpml-top-bar__item">
        <a href="http://domain.com/en/">
            <img src="https://dummyimage.com/24x18/000000/ffffff.jpg" alt="">
        </a>
    </div>
    <div class="mh-wpml-top-bar__item">
        <a href="http://domain.com/es/">
            <img src="https://dummyimage.com/24x18/cccccc/ffffff.jpg" alt="">
        </a>
    </div>
</div>

5. Change below links to your domain and folders:

http://domain.com/en/
http://domain.com/es/

6. Change below links to flags images

https://dummyimage.com/24x18/cccccc/ffffff.jpg
https://dummyimage.com/24x18/000000/ffffff.jpg

It will look like this: