Is there a way to save a form design as a theme to apply to another existing form?

You can save your form design as a theme by adding a Theme to our Theme Store: http://www.jotform.com/mythemes. Select "Show Only to Me" to unpublish the form in our theme store and make it available for you only. Please, check the guide below for more information:

https://www.jotform.com/blog/form-design-submissions/

If you have any question or issues, please do not hesitate contacting us. We will be glad to assist you.