Unfortunately this is not (easily) possible because the masonry gallery loads the data via ajax and if you randomize the slides you'll get many duplicate images (in the worst case the same images will be loaded over and over again when the user scrolls just because the "random" order selects them). However if you don't care about this drawback you can replace following code in includes/helper-slideshow.php:
function retrieve_post_images()
{
global $avia_config;
$unqiue_id = avia_post_meta($this->id, 'gallery_image');
$attachment_holder = avia_get_post_by_title( "avia_smart-gallery-of-post-".$unqiue_id);
if(empty($attachment_holder['ID'])) return;
$attachments = get_children(array('post_parent' => $attachment_holder['ID'],
'post_status' => 'inherit',
'post_type' => 'attachment',
'post_mime_type' => 'image',
'order' => 'ASC',
'orderby' => 'menu_order ID'));
with:
function retrieve_post_images()
{
global $avia_config;
$unqiue_id = avia_post_meta($this->id, 'gallery_image');
$attachment_holder = avia_get_post_by_title( "avia_smart-gallery-of-post-".$unqiue_id);
if(empty($attachment_holder['ID'])) return;
$attachments = get_children(array('post_parent' => $attachment_holder['ID'],
'post_status' => 'inherit',
'post_type' => 'attachment',
'post_mime_type' => 'image',
'orderby' => 'rand'));
Otherwise you need some code which checks for duplicates and removes them from the ajax response - however this requires some work and a skilled coder/freelancer.