There's an easy way if (and only if) you're developing an extension:
chrome.windows.create({
url: "http://www.google.com",
incognito: true
});
It requires tabs permission in the manifest, but that's it.
Note that the above has the user consent to allowing the extension to enter incognito mode, among other tab-related permission. I can't tell 100% whether you're developing an extension -- I assume not -- but in any case that's the extension solution and there isn't one otherwise.
