I have a solution for you! I used the code from the bottom of Function Reference/get pages
and figured out by trial and error that <?php echo the_field('your_field_id', $page->ID); ?> does the trick to display field data from the child pages.
Final code (including post thumbnail if you want):
<?php
$mypages = get_pages( array( 'child_of' => $post->ID, 'sort_column' => 'post_date', 'sort_order' => 'desc' ) );
foreach( $mypages as $page ) {
$content = $page->post_content;
if ( ! $content ) // Check for empty page
continue;
$content = apply_filters( 'the_content', $content );
?>
<?php echo get_the_post_thumbnail($page->ID); ?>
<h2><a href="<?php echo get_page_link( $page->ID ); ?>"><?php echo $page->post_title; ?></a></h2>
<p>Custom field info: <?php echo the_field('your_field_id', $page->ID); ?> </p>
<div class="entry"><?php echo $content; ?></div>
<?php
}
?>
