I got this sorted via email support, thank you very much. This is what the result looks like:
<?php
// if 'file' repeater has rows
if( have_rows('file') ): ?>
<!-- files select button -->
<button onclick="download()" type="button">Download</button>
<div id="download">
<!-- files select list -->
<?php
// loop through the 'file' rows of data
while ( have_rows('file') ) : the_row();
$files = get_sub_field('files');
$file_name = get_sub_field('file_name'); ?>
<!-- display file name with URL in download list -->
<a href="<?php echo $files['url']; ?>" target="_blank"><?php echo $file_name; ?></a>
<?php
// endwhile loop for 'file' repeater
endwhile; ?>
</div>
<?php
// else if 'file' repeater has no rows
else :
// no rows found
endif;
