You can access JSON data for a customer or a customer's order at the following endpoints.  If you have your shop set up to require logins, this will require the customer to be logged in when making the API call to get the data.

 
For all digital goods for a specific customer https://{{YOUR_SHOP_URL}}/apps/downloads/orders/{{customer.id}}.js

This will return JSON in the following format:

{
  pagination: {
    page: 1,
    per_page: 15,
    size: 54
  },
  orders_with_files: [
    {
      id: 5328511,
      order_number: 68592,
      delivery_url: "http://YOUR_SHOP_URL.myshopify.com/....",
      line_items_with_files: [
        {
          product: {
            title: "title"
            id: 1234555555
          },
          variant: {
            title: "title"
          },
          delivery_url: "http...",
          files: [{filename: .., filesize: .., download_url: "..",...}, {}],
          videos: [{title: "", ...}, {}],
          collections: [{...}, {...}]
        }
      ]
    },
    {...}, {...}...//Additional order details
  ]
}