I don't know much about VNC but you should be able to configure a script to run at startup if you can configure a program to run, say a .bat or .sh file.
Within this file you have a few ways of launching Chrome with a specific URL:
1. Shortcut files, and choosing one randomly.
You could have many in a folder, and your startup script chooses one at random.
╔══════════╦════════════════╦═════════════════════════════════╗
║ Protocol ║ Target ║ Result ║
╠══════════╬════════════════╬═════════════════════════════════╣
║ HTTP ║ www.google.com ║ googlechrome://www.google.com/ ║
║ HTTPS ║ www.google.com ║ googlechromes://www.google.com/ ║
╚══════════╩════════════════╩═════════════════════════════════╝
2. Launching Chrome directly with a random URL.
Make a script to pass the following, you can specify incognito by using the -incognito flag.
chrome.exe https://google.com