Adding functionality to a form button that would load user details / corresponding field data for "autofill"
Take a look at how Commerce Addressbook solves these same requirements: https://www.drupal.org/project/commerce_addressbook.

There is a demo video on the project page: https://commerceguys.com/blog/commerce-module-tuesday-commerce-addressbook.

I think if you dig through the module code of that module, you'll find all the logic and code examples you'll need to pull off a similar solution on your custom form.

If you want to see this in action on a local setup, I recommend installing commerce kickstart with commerce addressbook to see how the addresses are organized. 

Good luck, Jason