Maybe you need to update the app? On an iPhone it's pretty obvious. Now that I chose the award, it's visible under the "MY AWARDS" button when you scroll to the bottom. That button may have said something different before I selected the award. You definitely only need one delivered referal. That's all that I have and it let me choose the signature charger and provide a shipping address.
Edit:
Maybe I tapped on the "i" inside the circle describing the "next award" to order it. I can't remember, but it didn't take long at all with the phone app. I tried a lot longer and harder on the website and made no progress.