You can add your div every after 2 posts like this.
<?php $count = 1; // add this before loop ?>
<?php
// add this inside the loop
if ($count % 3 == 0) :
echo 'YOUR IMAGE DIV HERE';
endif; $count++; ?>
So, it will be something like this.
<?php $args = array( 'post_type' => 'galleries');
$queryone = new WP_Query( $args );
$count = 1;
while ($queryone -> have_posts()) : $queryone -> the_post(); ?>
<?php if ($count % 3 == 0) :
echo 'YOUR IMAGE DIV HERE';
endif; $count++; ?>
<section class="feature-third">
<a href="https://wordpress.stackexchange.com/questions/271169/<?php echo get_permalink( $ID ); ?>" title="<?php the_title( ); ?>">
<div class="feature-captions"><?php $current_cat_id = the_category_ID(false); echo '<p class="category-link">' . get_cat_name($current_cat_id) . '</p>'; ?><h2><?php echo get_the_title( $post->ID ); ?> </h2><?php if( get_field('subtitle') ): ?><p><?php the_field('subtitle'); ?></p><?php endif; ?></div>
<?php the_post_thumbnail('full'); ?>
</a>
</section>
<?php endwhile; ?>