I think this is not possible with the API functions provided by ACF. I would try to save the values to a temporary array first and then sort the values inside the array with php (using krsort() for example).
Something like this (just to give an idea):
while(has_sub_field('in_the_news')) {
$date = get_sub_field('published_date');
// $date = 19881123 (23/11/1988)
// extract Y,M,D
$y = substr($date, 0, 4);
$m = substr($date, 4, 2);
$d = substr($date, 6, 2);
// create UNIX
$time = strtotime("{$d}-{$m}-{$y}");
$tmp_array[$time] = array(
'link' => get_sub_field('link'),
'title' => get_sub_field('title'),
'publisher' => get_sub_field('publisher'),
'date' => date('d/m/Y', $time)
);
}
krsort($tmp_array);
foreach($tmp_array as $entry ) {
// your html ...
}
PS: It’s always better to save timestamps in a proper format (i.e. unix timestamp) in the first place if somehow possible. 19881123
is a strange date format.