Custom Post type slider with thumbnail navigation

Follow this flow:
Define an empty array $nav_img = array(); outside the loop.

Inside the loop while you fetch the featured image, push the URL to the array too like this $nav_img[]='your_image_here' ;

Then inside <div class="slider-nav-thumbnails"></div> you can simply do a for each loop to set the images as thumb.

UPDATE:

Here I added example with your existing code.

<div class="row">
    <div class="large-7 medium-8 columns">
        <div id="slider">

        <?php
        $the_query = new WP_Query( array(
            'post_type' => 'cpt',
            'tax_query' => array(
                array (
                    'taxonomy' => 'customtax',
                    'field' => 'slug',
                    'terms' => 'mytax',
                )
            ),
        ) );

        $nav_imgs = array();

        while ( $the_query->have_posts() ) :
            $the_query->the_post();
            $nav_imgs[] = get_the_post_thumbnail_url(get_the_ID(),'thumbnail'); 
          ?>
        <figure> 
            <img src="https://wordpress.stackexchange.com/questions/349647/post thumbnail url" alt="One">
            <figcaption>Post  content, title, custom fields etc</figcaption>
        </figure>
        <?php 
        endwhile;
        wp_reset_postdata();
        ?>
        </div>
        <!-- THUMBNAILS -->
        <div class="slider-nav-thumbnails">
            <?php 
                foreach($nav_imgs as $nav_thumb) {
                   echo '<div><img src="'.$nav_thumb. '"></div>';
                }
             ?>
        </div>
    </div>
</div>