I tested this out and then it wouldn't let me exit kiosk mode. I had to Cmd+Q to get out of Google Chrome. Save the following to a script, something like ChromeKiosk.sh and chmod +x ChromeKiosk.sh to get it to run.
#!/bin/bash
open "/Applications/Google Chrome.app" --args --kiosk http://www.google.com.au
This will open Google Chrome to the http://www.google.com.au webpage. Change it as you need. Copy and paste the rest of the script
If you want to turn it into an AppleScript so that you can create an application that can in turn be automatically run each time the computer reboots to a default specified user, use the following code and when you save the script, change it's type to Application
do shell script "/bin/bash open \"/Applications/Google Chrome.app\" --args --kiosk"
It's requires the \ (escape sequence) before the " because of the way the shell reads the spacing between the words Google and Chrome in the filename. You can also write it as
do shell script "/bin/bash open /Applications/Google\\ Chrome.app --args --kiosk"
It's just that I've never favoured the look of seeing a escape before a backslash. It's too messy. Stick with either the BashScript option at the top or use the 1st of 2 AppleScript lines and save it as an Application type.
Apple does not allow command line access on iOS. This may be possible with a jailbroken device, but I have never investigated that.
I looked for a setting in Chrome to allow this and I could not find one on the Desktop settings panel, or in the advanced settings. My thought was that the setting would be synced to iOS and the iOS app would honor that request.
The last thing I can think of is to be in an incognito tab when closing the app, that way it will restore that tab when restarting the app. This worked in my testing, although it remembered and reloaded the page it was on.
Best Answer
This can be achieved with the following in script editor:
Save it as an application, throw the alias in the dock. Tested this in 10.6.8.
Only works if you don't have chrome open already.