How do I designate favorites to allow calls from in Do Not Disturb?

Go to settings menu and select "Do Not Disturb". Once in the "Do Not Disturb" setting scroll down and find "Phone, Allow Calls From". Click that and select "Favorites". If your contact is marked as a "Favorite", you will received calls only from that person when the phone is in Do Not Disturb mode.

In the Phone app on the iPhone, there is a Favorites list, and you can add or edit people in that list. After they are selected there, you can go to Settings>Do Not Disturb, and under Phone, Allow Calls From, and select Favorites.