Hi SP,
You can think of the Rest API as being atomic and Alteryx Designer as an interactive application that is leveraging to a large extent the REST API. As a result, there is no API call or documented and supported means to embed the designer into your own application framework.
I would suggest sharing this idea so your peers can upvote it and let the product team know.
You can do this by going to Participate > Ideas > AACP in the menu and entering the idea.
Cheers,
Sebastian