Short answer – Go to TestFlight directly on Mobile Safari and use the TestFlight CocoaPod.
We got TestFlight working on the latest iOS 7 build. The TestFlight “app” that installs doesn’t work, but manually visiting the TestFlight site in Mobile Safari allows you to install the profile and load the app. Nothing special needed. It sometimes takes a few tries loading the profile to get it to actually load.
Also, loading our apps into TestFlight wasn’t working, so we started using the TestFlight CocoaPod and it works great.