Using WP Color Picker in Repeatable Fields

It’s hard to know for sure, since you don’t include the markup you’re output for the metabox nor the JS you’re using to clone. But, the following simplified setup seems to work for me:

metabox markup

<label for="my_field">
    My Color Picker Field
</label>
<input name="my_field" id='my_field' type="text" class="my-colorpicker" />
<a href="#" class="clone-it">Add Another Color Picker</a>

JS

(function ($) {
    // turn the field into a colorpicker
    $('.my-colorpicker').wpColorPicker () ;

    $('.clone-it').click (function () {
        // clone the field in question
        var field = $(this).prev ('.wp-picker-container').find ('.my-colorpicker').clone () ;

        // set the cloned field's value to ''
        // so it starts off without a specific color
        $(field).val ('') ;

        // your code to mod the cloned field's name, etc goes here 

        // add the cloned field to the metabox
        $(this).before (field) ;

        // turn the cloned field into a colorpicker
        $(field).wpColorPicker () ;
        }) ;

})(jQuery)