Out of the box, the Oxygen Gallery element cannot show images from a gallery field in an Advanced Custom Fields repeater. You need to use a code block in your loop (or in your Oxygen Builder Repeater element if you’re using that).
You’ll also need a lightbox solution. Again, either a custom code solution or some 3rd party Oxygen addons let you define a custom gallery/lightbox source.
The custom code for use in your ACF Repeater to view your gallery images you can find below. Make sure to change ‘gallery’ to your gallery field name.
<?php
$images = get_sub_field('gallery');
if( $images ): ?>
<ul class="thumb-gallery">
<?php foreach( $images as $image ): ?>
<li class="thumb-gallery-li">
<img src="<?php echo $image['sizes']['thumbnail']; ?>" data-large="<?php echo $image['sizes']['large']; ?>" alt="<?php echo $image['alt']; ?>" />
<p><?php echo $image['caption']; ?></p>
</li>
<?php endforeach; ?>
</ul>
<?php endif; ?>