If you are unable to install the Apple Watch Member ID App please refer to the below:
App is not installing from my Phone to my watch
If the app is not installing from your phone to your watch then the best is to load the App store from your watch and search for the app and install it directly from the watch.
If your watch does not have an App store option, it normally means you are not running the latest Watch operating system (ie: WatchOS 6 or greater)
App is not installing on my watch - it just spins endlessly but doesn't install
Try restarting your watch. Instructions on restarting your watch can be found here: