This is guess, but I think I know what you are looking for.
<?php $bg_color = get_sub_field('div_background_color'); ?>
<div style="background-color:<?php echo $bg_color; ?>">
<!-- content -->
</div>
Further down the page in your other layout you would just need to <?php echo $bg_color; ?> in the bg style declaration.
Let me know if I am way off base with your request, but I’m hoping I got it right 🙂