I just uploaded a new build to test flight, that fixes a minor bug. This may fix the issue that was preventing you form installing it, but It sounds like you might need to reinstall the test flight profile:
1. Open the Settings app.
2. Select General
3. Select Profile - 2nd to last item
4. If Testflight profile is listed, select it, then select delete. You may have to delete it multiple times to get it to delete.
5. Open Safari
7. Sign in
8. Tap the button in the upper Left to open the menu.
9. Select Devices - Under settings
10. Tap “Reconnect Current Device”
After that you should be able to install the latest beta by visiting
http://testflightapp.com or see my email from this morning about the newest build.
This same procedure applies for anyone else that has a new device, and restored it from a backup of an old device.