this example is not really using external authentication. It's just passing some sort of unique id to the authenticator.
in order to correctly use external authentication you should have a server-side component that build an external authentication token (that looks like "exx=bunch-of-base64-stuff") and pass it to the AdobeHSAuthenticator.
the authToken parameter should be THE RESULT of Session.getAuthenticationToken that you called server-side.
The Flex example doesn't run without the appropriate server-side counterpart (the purpose of External Authentication is that you authenticate your users on your server, and then create a token to pass to our server).
What are you running server-side and how did you "make" your authentication token ?