You are going up from current element, then looking within that parent for all the images.... you only want to find
within the current element
Change to:
/* find within "this"*/
$(this).find('img.badge-item-animated-img').attr('src', src);
Edit: clcik on jpg, change src of GIF:
$('.badge-item-img').click(function(){
$(this).parent().next().find('img.badge-item-animated-img').attr('src',function(i,src){
/* replace src with same vale so GIF refreshes*/
return src;
});
})