You need to call .uniform()
again after you clone it so it can initialize the plugin on the new elements:
// Uniform every form element
$(function () {
// Show browser information
$('input, select').uniform();
$('form').on('click', '.button', function () {
var el = $(this).parents('.formElement');
$(el).clone().insertAfter($(el));
$('input, select').uniform();
});
});