If you’re looking for this to be fully automated, I would use Integromat or Zapier to do that for you. After a new record gets added via the form, Integromat or Zapier can add all the linked values into your record for you.
Otherwise, there’s a partially-automated way that you could do this. If you write a custom JavaScript to add the linked values into your record for you, you could trigger the JavaScript by clicking on a button in the record after it’s been created.