To enable incognito tabs you must set two flags in chrome:
chrome://flags/#cct-incognito
chrome://flags/#cct-incognito-available-to-third-party
You will need to copy the above links and open them in Chrome as they cannot be directly linked
Along with the the "incognito custom tabs" option in Sync under "Link Handling".
Be warned this is a little buggy...
Finally this only works with Chrome and not Firefox.