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.