The official HDHomeRun app will NOT work on the “SELECT” version of the Fire TV stick.
The “Select” version is a cheaper, crappier version of the Fire TV devices, and should be avoided for many reasons, including that it doesn't work with the HDHomeRun app. At this time other versions of Fire TV are not currently affected and should be okay to use.
Optional: Add the HDHomeRun app to the home screen
The HDHomeRun will attempt to automatically scan for channels the first time it is connected to power, and will occasionally do a background scan every few days, but you may still need to run an initial channel scan.
The majority of Fire TV devices run an OS based on Android called Fire OS. The Fire TV Stick 4K that ends with “Select” in its name is a new and runs a different OS, and as such, the current official HDHomeRun app (and many other streaming apps) is not compatible with it.