Apps appear to download and then the button state switches back to “install” and the app icon on the device indicates “waiting”
Update: I am "extremely concerned" that as soon as I applied the IOS update for 14.2 to the iPad test device, Test Flight worked like a charm. I am 100% certain that was the fix because it failed immediately before the update and worked immediately after the update. It was not caused by a reboot, because I had rebooted the device multiple times in an attempt to install from Test Flight.
I don't know if that is because of an Apple desire to force the device to be updated or an indication that the version will only work on other devices that have been updated to 14.2. Interestingly, the Test Flight release did install successfully on a test iPhone that is not running 14.2. Hopefully, Apple will realize that developers need to keep later versions of their operating system installed on test devices in order to validate backwards compatibility.
I don't know if that is because of an Apple desire to force the device to be updated or an indication that the version will only work on other devices that have been updated to 14.2. Interestingly, the Test Flight release did install successfully on a test iPhone that is not running 14.2. Hopefully, Apple will realize that developers need to keep later versions of their operating system installed on test devices in order to validate backwards compatibility.