WordPress Customizer Flexible List Control | http://www.ibenic.com/wordpress-customizer-flexible-list-control

control.css

.removeInput {
  position: absolute;
  right: 15px;
  z-index: 999;
  background-color: white;
  display: block;
  border-radius: 10px;
  font-size: 10px;
  line-height: 20px;
  width: 20px;
  height: 20px;
  text-align: center;
  margin-top: 2px;
  cursor: pointer;
}

control.js

function serialize(e){var r,t,n,a="",i="",o=0,c=function(e){var r=0,t=0,n=e.length,a="";for(t=0;n>t;t++)a=e.charCodeAt(t),r+=128>a?1:2048>a?2:3;return r};switch(_getType=function(e){var r,t,n,a,i=typeof e;if("object"===i&&!e)return"null";if("object"===i){if(!e.constructor)return"object";n=e.constructor.toString(),r=n.match(/(\w+)\(/),r&&(n=r[1].toLowerCase()),a=["boolean","number","string","array"];for(t in a)if(n===a[t]){i=a[t];break}}return i},type=_getType(e),type){case"function":r="";break;case"boolean":r="b:"+(e?"1":"0");break;case"number":r=(Math.round(e)===e?"i":"d")+":"+e;break;case"string":r="s:"+c(e)+':"'+e+'"';break;case"array":case"object":r="a";for(t in e)if(e.hasOwnProperty(t)){if(a=_getType(e[t]),"function"===a)continue;n=t.match(/^[0-9]+$/)?parseInt(t,10):t,i+=this.serialize(n)+this.serialize(e[t]),o++}r+=":"+o+":{"+i+"}";break;case"undefined":default:r="N"}return"object"!==type&&"array"!==type&&("string"===type&&-1!==r.indexOf("}")||(r+=";")),r}

(function($){

	$(document).ready(function(){
    // Our JS Code will go here
  });

})(jQuery);

control.php

<?php

if( class_exists( 'WP_Customize_Control' ) ):
	class SNT_List_Control extends WP_Customize_Control {
		public $type = 'list';

		public function render_content() {
      // Our HTML will go here
		}
	}
endif;

control2.js

(function($){

	$(document).ready(function(){

		$(document).on('click', ".list-control-add", function(){
			
			var id = $(this).attr("data-id");
			var list = $("#list-control-" + id );
			list.append('<div class="listinput"><span class="removeInput" >X</span><input type="text" value="" /></div>');
		});


		$(document).on('click', ".list-control-confirm", function(){
			 
			var id = $(this).attr("data-id");
			var list = $("#list-control-" + id ); 

			var values = [];
			list.children().each(function(){
				var value = $(this).find('input').val();
				values.push(value);
			});

			$("#list-input-" + id ).val( serialize( values ) ).trigger("change");

			
		 });

		$(document).on('click',".removeInput", function(){
		 	var $parent = $(this).parent(".listinput");
		 	$parent.remove();
		});

	});

})(jQuery);

control2.php

<?php

 // ...
		public function render_content() {
      // Get Value from this setting
			$values = $this->value();
      
      // if is reliazed, unserialize it so that we can use it as array
			if ( is_serialized( $values ) ) {
				$values = unserialize( $values );
			}
      
			?>	
			 
			<label>
				<span class="customize-control-title"><?php echo esc_html( $this->label ); ?></span>
			</label>

			<div class="control-list" id="list-control-<?php echo $this->id; ?>">
				 	<?php
				 		if( is_array( $values ) ) {
              // For each $values, create an input
				 			foreach ($values as $value ) { ?>
				 				 <div class="listinput">
									<span class="removeInput" >X</span>
									<input type="text"  value="<?php echo $value; ?>" placeholder="" />
								</div>
								<?php
				 			}
				 		}
				 	?>
			</div>
      <!-- Button for adding new input -->
			<button type="button" data-id="<?php echo $this->id; ?>"  class="button list-control-add button-default">Add</button>
			<!-- Button to confirm the list -->
      <button type="button" data-id="<?php echo $this->id; ?>"  class="button list-control-confirm button-primary">Confirm List</button>
			
			<?php 
        // If it's not serialized, serialize it to save in input
				if ( ! is_serialized( $values ) ) {
					$values = serialize( $values );
				}
			?>
      
      <!-- Input that is the control setting data -->
			<input  <?php echo $this->link(); ?> type="hidden" id="list-input-<?php echo $this->id; ?>" name="<?php echo $this->id; ?>" value="<?php echo $values; ?>" placeholder="" />
		 
		<?php
		}
// ...

enqueue.php

<?php

add_action( 'customize_controls_enqueue_scripts', 'snt_customizer_controls_scripts' );
function snt_customizer_controls_scripts() {
	  wp_enqueue_script( 'custom_snt_control_js', get_stylesheet_directory_uri() . '/js/customizer-controls.js', array( 'customize-preview', 'jquery' ) );
	  wp_enqueue_style( 'custom_snt_control_style', get_stylesheet_directory_uri() . '/css/customizer-controls.css' );

}

serialize.js

function serialize(mixed_value) {
  //  discuss at: http://phpjs.org/functions/serialize/
  // original by: Arpad Ray (mailto:[email protected])
  // improved by: Dino
  // improved by: Le Torbi (http://www.letorbi.de/)
  // improved by: Kevin van Zonneveld (http://kevin.vanzonneveld.net/)
  // bugfixed by: Andrej Pavlovic
  // bugfixed by: Garagoth
  // bugfixed by: Russell Walker (http://www.nbill.co.uk/)
  // bugfixed by: Jamie Beck (http://www.terabit.ca/)
  // bugfixed by: Kevin van Zonneveld (http://kevin.vanzonneveld.net/)
  // bugfixed by: Ben (http://benblume.co.uk/)
  //	input by: DtTvB (http://dt.in.th/2008-09-16.string-length-in-bytes.html)
  //	input by: Martin (http://www.erlenwiese.de/)
  //		note: We feel the main purpose of this function should be to ease the transport of data between php & js
  //		note: Aiming for PHP-compatibility, we have to translate objects to arrays
  //   example 1: serialize(['Kevin', 'van', 'Zonneveld']);
  //   returns 1: 'a:3:{i:0;s:5:"Kevin";i:1;s:3:"van";i:2;s:9:"Zonneveld";}'
  //   example 2: serialize({firstName: 'Kevin', midName: 'van', surName: 'Zonneveld'});
  //   returns 2: 'a:3:{s:9:"firstName";s:5:"Kevin";s:7:"midName";s:3:"van";s:7:"surName";s:9:"Zonneveld";}'

  var val, key, okey,
	ktype = '',
	vals = '',
	count = 0,
	_utf8Size = function(str) {
	  var size = 0,
		i = 0,
		l = str.length,
		code = '';
	  for (i = 0; i < l; i++) {
		code = str.charCodeAt(i);
		if (code < 0x0080) {
		  size += 1;
		} else if (code < 0x0800) {
		  size += 2;
		} else {
		  size += 3;
		}
	  }
	  return size;
	};
  _getType = function(inp) {
	var match, key, cons, types, type = typeof inp;

	if (type === 'object' && !inp) {
	  return 'null';
	}
	if (type === 'object') {
	  if (!inp.constructor) {
		return 'object';
	  }
	  cons = inp.constructor.toString();
	  match = cons.match(/(\w+)\(/);
	  if (match) {
		cons = match[1].toLowerCase();
	  }
	  types = ['boolean', 'number', 'string', 'array'];
	  for (key in types) {
		if (cons === types[key]) {
		  type = types[key];
		  break;
		}
	  }
	}
	return type;
  };
  type = _getType(mixed_value);

  switch (type) {
	case 'function':
	  val = '';
	  break;
	case 'boolean':
	  val = 'b:' + (mixed_value ? '1' : '0');
	  break;
	case 'number':
	  val = (Math.round(mixed_value) === mixed_value ? 'i' : 'd') + ':' + mixed_value;
	  break;
	case 'string':
	  val = 's:' + _utf8Size(mixed_value) + ':"' + mixed_value + '"';
	  break;
	case 'array':
	case 'object':
	  val = 'a';
	  /*
		if (type === 'object') {
		  var objname = mixed_value.constructor.toString().match(/(\w+)\(\)/);
		  if (objname === undefined) {
			return;
		  }
		  objname[1] = this.serialize(objname[1]);
		  val = 'O' + objname[1].substring(1, objname[1].length - 1);
		}
		*/

	  for (key in mixed_value) {
		if (mixed_value.hasOwnProperty(key)) {
		  ktype = _getType(mixed_value[key]);
		  if (ktype === 'function') {
			continue;
		  }


		  okey = (key.match(/^[0-9]+$/) ? parseInt(key, 10) : key);
		  vals += this.serialize(okey) + this.serialize(mixed_value[key]);
		  count++;
		}
	  }
	  val += ':' + count + ':{' + vals + '}';
	  break;
	case 'undefined':
	  // Fall-through
	default:
	  // if the JS object has a property which contains a null value, the string cannot be unserialized by PHP
	  val = 'N';
	  break;
  }
  if (type !== 'object' && type !== 'array') {
	  if ( type === 'string' && val.indexOf('}') !== -1 ) {
	  } else {
			val += ';';
		}
  }
  return val;
}