A recent report from Android Police revealed that YouTube is testing Incognito mode for its Android version. This was first spotted in an APK teardown earlier this year in January.
As of now this isn’t available for any user group as a test version and seems to be a server side test. The incognito mode option can be found in the menu that can be accessed by clicking on the account Avatar located on the top right corner.
There isn’t any official confirmation from the team regarding this new feature.