Same here. Contacted Apple support but they are not responding. Google shows finds this issue spanning years, but nobody has a real solution.
When you open the Console.app -> iPhone -> Start Streaming -> Filter: TestFlight, then initiate the action to "Install" the app.
There will be some message like:
URL=https://testflight.apple.com/v2/accounts/xxxxx-xxxx-xxxx-xxxx-xxxxxxxx/apps/xxxxxxxxx/builds/xxxxx/install; code=404 <--
Followed by:
errorMessage = The requested app is not available or doesn’t exist., code = -1, serverCode = 200, serverFailureReason = Error Downloading Install Data
Given that the App is clearly listed in TestFlight and that the TestFlight app even shows the updated versions, it makes the impression that the requested install URL may not be correctly built and requested by the TestFlight app.