Set K2_DATE_FORMAT_LC with text is Y/m/d.
To display the date below title is "d/m/Y", you can edit modules/mod_jfslideshow/tmpl/bgslideshow.php. Modify:
$description = '<div class="container slidedescription"><h3>'.$dateEvent.'</h3><p>'.$locationEvent.'</p><div id="clock">'.date("Y/m/d", strtotime($dateEvent)).'</div>';
to:
$description = '<div class="container slidedescription"><h3>'.date("d/m/Y", strtotime($dateEvent)).'</h3><p>'.$locationEvent.'</p><div id="clock">'.date("Y/m/d", strtotime($dateEvent)).'</div>';
joomfreak