I got it working on an iPad mini running iOS 7 beta 5, that was previously used with testflight while running iOS 6. It seems that it will work under some circumstances. What I did:
- Unregistered the device from its connected testflight user account (actually this step might be irrelevant)
- Launched testflightapp.com from Safari, not from any icon placed on home screen. It has to be from Safari where the url bar is shown. From here I could install betas. However the device itself is not listed under any user and it is not activated. While trying to activate it, testflight app says the registering works OK, however it really fails.
So, it MIGHT work but it's clear that the people at testflight has some work to do.
More: I am unable to get it working with an iPhone 4 iOS 7 beta 5 at all. The iPhone has not previously been used with testflight and seems to require an activation through that profile (at testflight or Apple, not sure) but the activation fails and there's no app list coming up in Safari, just the activation sequence. The key here might be that the device must have been used with testflight before, while on iOS previous to 7.
It seems that using testflight with iOS 7 beta does not work and/or is not supported at the moment.
Not sure what happened here but I was using testflight with an iPad mini that had iOS6. When I just upgraded it to iOS 7, the testflight site loads on the device, however installs never process.