The messages you see are not an error. A framework is included twice in the bundle (once for Chrome, once for Chrome helper), and it tells you.
I tested the --kiosk and -kiosk arguments with both current Chrome and a build of Chromium from today and it never worked as written in the other thread.
I successfully passed --incognito as parameter, so if it were implemented, it would work this way.
Since the page you link to is the only information I could find on Chrome for Mac kiosk mode, I'd guess it's not yet implemented. If you read the comments over there, Andrew (the person answering) didn't test it himself, he queried the person asking for the name of the binary and perhaps just posted that and the windows command line parameter.
To start Chromium in full screen, write out the following AppleScript in AppleScript Editor:
tell application "Chromium"
activate
tell application "System Events"
key down {command}
key down {shift}
keystroke "f"
key up {shift}
key up {command}
end tell
end tell
If you use Chrome, replace "Chromium" with "Google Chrome".
Executing this script first starts Chromium, and then immediately enters full screen mode.
Testing the above script on OS X Lion, even without the new window animation enabled, didn't work. I had to add delay 0.1 to the script just after activate, so that the menu item was actually activated.
Run Skype.app, then use this command in terminal:
sudo /Applications/Skype.app/Contents/MacOS/Skype /secondary
Tested on Mac OS X Lion 10.7.4 and Skype 5.8.0.865.
Best Answer
I don't know why you don't have internet on the second instance, but I want to provide an alternative. In your browser, visit web.whatsapp.com and create a window shortcut. It will act like a secondary app.
In any Chromium browser you can do it at Settings > More Tools > Create Shortcut then make sure it will be in Window mode.