If you can't determine it from the user agent (Does the Kiosk mode browser send a different user agent string?) or the IP address (perhaps the Kiosks have a fixed IP range or use a specific proxy server?), then maybe you can do it via Javascript by measuring the screen size.
I believe that you can check the window size and screen size through the Javascript "navigator" object then compare those; if there are no decorations at all, then the browser is in kiosk or no-decorations fullscreen mode.
Mark