Wordpress - Adding Widget form fields dynamically

Interesting Question!
I've never seen repeatable fields used in Widgets. Giving a full Answer would require too much work/time, so I'll give you links to the resources I know, and hopefully you'll make this work and share the solution with us ;)

All this examples deal with Meta Boxes, you'll need to copy the jQuery scripts and adapt the post_meta to the Widgets case.

• Create more Meta Boxes as needed - WPSE Q&A

• Repeatable Custom Fields in a Metabox - Gist

  /**
   * Repeatable Custom Fields in a Metabox
   * Author: Helen Hou-Sandi
   *
   * From a bespoke system, so currently not modular - will fix soon
   * Note that this particular metadata is saved as one multidimensional array (serialized)
   */
  

• Repeatable Custom Fields in a Metabox - Another Gist example, no description given. This one is quite interesting as it has the code to sort the fields.

This is an example of a dynamic widget that renders two fields (image-id and url). if you enter an image-id and press "update", two new fields are added. I build it to create a slick slilder with images and linked url's.

<?php

class imp_image_slider extends WP_Widget
{
/**
 * imp_image_slider constructor.
 */
public function __construct()
{
    parent::__construct(false, $name = "Impulse Image Slider", array("description" => "Creates Slick Image Slider"));
}

/**
 * @see WP_Widget::widget
 *
 * @param array $args
 * @param array $instance
 */
public function widget($args, $instance)
{
// render widget in frontend
}


/**
 * @see WP_Widget::update
 *
 * @param array $newInstance
 * @param array $oldInstance
 *
 * @return array
 */
public function update($newInstance, $oldInstance)
{
    $instance = $oldInstance;
    $instance['images'] = array();
    $instance['urls'] = array();
    if (isset($newInstance['images'])) {
        foreach ($newInstance['images'] as $key => $value) {
            if (!empty(trim($value))) {
                $instance['images'][$key] = $value;
                $instance['urls'][$key] = $newInstance['urls'][$key];
            }
        }
    }

    return $instance;
}

/**
 * @see WP_Widget::form
 *
 * @param array $instance
 */
public function form($instance)
{
    $images = isset($instance['images']) ? $instance['images'] : array();
    $urls = isset($instance['urls']) ? $instance['urls'] : array();
    $images[] = '';
    $form = '';

    foreach ($images as $idx => $value) {
        $image = isset($images[$idx]) ? $images[$idx] : '';
        $url = isset($urls[$idx]) ? $urls[$idx] : '';
        $form .= '<p>'
            . '<label>Slides:</label>'
            . sprintf(
                '<input type="text" name="%1$s[%2$s]" value="%3$s" class="widefat" placeholder="Image ID">',
                $this->get_field_name('images'),
                $idx,
                esc_attr($image))
            . '</p>'
            . '<p>'
            . sprintf(
                '<input type="text" name="%1$s[%2$s]" value="%3$s" class="widefat" placeholder="Url">',
                $this->get_field_name('urls'),
                $idx,
                esc_attr($url))
            . '</p>';
    }

    echo $form;
}
}

add_action('widgets_init', create_function('', 'return register_widget("imp_image_slider");'));

?>