Received an invitation to install the new beta test version, but need a second invite if I am to test the iPad Mini 2. Code can only be redeemed once.
You should be able to simply install TestFlight on your other device and tap on the same activation email.
Did that before I emailed this request and on the iPad Mini it reports that the invitation has been redeemed and to request another invite from the developer.
I've tested other apps through TestFlight and that seems to be the way it works.