A gallery field stores an array of post ID’s. To add an image you first need to get the value and add the new ID value to it.
$gallery = get_field('gallery', get_the_ID(), false); // get unformatted value
if (empty($gallery)) {
$gallery = array();
}
$gallery[] = get_post_thumbnail_id(get_the_ID());
update_field('gallery', $gallery, get_the_ID());