There are two basic ways to do this.

1. Use .on() to bind to the dynamic element
2. Store reference to the object in a Variable and assign click() callback to the object

Here is an example of the latter.

$(function() {

  // Multiple images preview with JavaScript
  var multiImgPreview = function(input, imgPreviewPlaceholder) {

    if (input.files) {
      $("#multipleImageUpload").on("change", function(e) {
        var filesAmount = input.files.length;

        $.each(input.files, function(i, file){
          var reader = new FileReader();

          reader.onload = function(event) {
            var pip = $("<span>", {
              class: "pip"
            }).appendTo(imgPreviewPlaceholder);
            var icon = $("<span>", {
              class: "remove_icon"
            }).html("Remove").insertAfter(pip);
            var img = $("<img>", {
              src: event.target.result,
              title: ""
            }).insertAfter(icon);
            
            icon.click(function() {
              $(this).parent(".pip").remove();
            });
          }

          reader.readAsDataURL(file);
        }
      });
    }
  };

  $(document).on('click', '#multipleImageUpload', function() {

    // add to preview
    multiImgPreview(this, 'div.imgPreview');

    //clone
    var originalInput = $(this),
      cloned = originalInput.clone();

    // move
    originalInput.attr("id", Date.now());
    originalInput.removeClass('multipleImageUpload');
    originalInput.appendTo($('#multipleFilesPH'));

    cloned.attr("id", "multipleImageUpload");
    cloned.insertAfter($('#multipleFilesPH'));

    originalInput = null;
    cloned = null;

  });
});

This uses the jQuery ability to create DOM elements on the fly from the provided string of raw HTML. See More.

If you want to bind a click callback to that specific element, you can store the resulting Object in a variable and use that to bind the event to that object alone.

I switched the attribute to Class as you will likely have more than 1 element with this ID, hence why it would not be Unique from other elements. You might end up with 3 or 4 elements with the same ID.