However if you want to broadcast your Chrome Tab in incognito mode it is not possible by default. This is not due to an issue with the Google Cast extension, instead for security reasons chrome disables extensions in incognito mode. But you can choose to enable extensions to run in incognito mode manually through chrome settings.
Cast Extension not available in Incognito mode
Steps to enable cast extension in incognito mode
1. Click on Settings -> Tools -> Extensions
2. Scroll down until you find Cast Extension and check Allow in incognito
3. Now launch Chrome in incognito mode and you’ll find Cast icon appear on the toolbar
Now enjoy sharing your tabs to Chromecast even in incognito mode.