When a user adds their first device to TestFlight and creates their account, it installs an app that’s a wrapper for the mobile version of the TestFlight site. This provides a convenient way for them to install any builds the developer sends them without having to go through their e-mail.
When they go through the process again on another device, it doesn’t install the app – only the TestFlight over-the-air provisioning profile.
How can they get that app on their second device, or if they inadvertently delete it from the first one? They can add a Mobile Safari shortcut for the page to their home screen, but that’s not quite the same as it then opens the page in mobile Safari. Is there any other way?
Try following these instructions from TestFlight.