How can I disable Chrome's incognito mode without rooting Android? Is there a way to disable Incognito Mode in Chrome without rooting? My phone is running Android Lollipop.
Disclaimer

This answer is pointless.  Once you've read the end of my answer, you will see why.

My answer

I personally have tried Qustodio's "Block Incognito Browsing" feature.  (I was using a phone running Android 4.1.2 and a recent version of Google Chrome.)

It didn't work at all.

Incognito browsing still worked perfectly, and was not blocked or even hindered whatsoever.  Even after an hour or more, Qustodio had no idea that I was using Chrome's incognito mode.

In a help center article, Qustodio LLC does admit:


  Please note that our incognito blocking feature is still experimental.


If you want to prevent incognito browsing, I see a few options:


You could lock down the device completely (though this is almost impossible to do correctly) and then to make sure that the only browser which the user can access is a browser which is incapable of incognito browsing.
Or you could use Norton Family's incognito detection.  If Norton Family alerts you that incognito has been used, perhaps you could confiscate the device from its user for a day or two.  (Norton Family claims to be able to email you after someone uses incognito mode on the device.  But I've never tested it, and I don't know whether or not it would work reliably.  You should test the feature on a few separate occasions before relying upon it.)
You could try Qustodio.  Even though their (experimental) incognito-blocking feature didn't work for me, maybe it will work for you.
If you are willing to root your phone, this may provide you with a new, additional option for disabling incognito mode.  Remember that you can unroot your phone afterwards.


Why this answer is pointless

Yet all this is pointless.  The user can use the browser's "Clear History" tool, or Android's application manager, to clear the browsing history &mdash; anytime he wants to.

Why would anyone want to disable incognito mode?