This is a strange issue we're currently having.
We uploaded a new version of our application to itunes connect, and we sent it to the internal testers. However, only those where we installed some version of the application directly through XCode at some point are the ones who can install it via testflight.
Our devices where the app has never been directly installed through XCode cannot install the game right now through testflight (the download gets to around 98% and the says that it was unable to install, even if they had downloaded a previous version of the application through Testflight successfully at some point).
So, I'm assuming, maybe there's something in the XCode settings? It seems like something quite specific.
You should sign your application with an Ad-hoc profile, not the developer and not the AppStore one. To make sure it is about provision or certificate signing, with your device connected to computer, in XCode, open device manager and see log while you are trying to install app via Testflight.