This issue appears to be resolved as of a few minutes ago. I was able to install the testflight builds that I've been trying all day.

We are having this issue as well. Trying to install from previous builds also fails with the same error. Looking in the console logs I found this: TestFlight Install Request Completed (status = Failed): { bundleID = , appType = 2, version = , currentTaskStatus = 22, previousTaskStatus = 9, installStatus = 0, reachedTerminalStatus = 1, reachedFailureStatus = 1, reachedCancelledStatus = 0, percentComplete = 0.000000, userFailureReason = <TFError: 0x281ab1560>: errorMessage = The profile can’t be installed. Try again., code = -1, serverCode = 605, serverFailureReason = Error Downloading Install Data, persistentIdentifier = 0, installID = (null) }