Android - On Android, how to disable Google Chrome's incognito mode

If you have rooted your phone, you can build and push a system ChromeCustomizations app. This installs a content provider which, among other things, allows disabling Incognito mode in Chrome.

This uses the officially-supported way that device manufacturers use in order to control the starting page and default bookmarks of Chrome on their devices.

You could try Incoquito - it's a paid app and allows you to either automatically close all incognito tabs when the screen turns off or to disable incognito browsing altogether by preventing incognito tabs from being opened at all. It includes a monitoring mode as well as logging of events/activities related to incognito browsing in Chrome as well as the ability to hide the app from the launcher. It also includes the following experimental features (as requested by several parents):

• Log videos played within the YouTube app
• Uninstall detection & prevention
• Android settings guard
• Block access to YouTube app

Disclosure: I am the developer of Incoquito.