Google Family Link
If you set Google Family Link to protect an Android device, it will automatically disable Google Chrome's incognito mode on that device. (Google says so in this article. I myself have tried Family Link and verified that the article is correct.)
Family Link can also do Web filtering, screen-time monitoring, and device-location tracking. But these features are optional; you may disable them if you wish.
The usual Family Link setup is as follows: One device (a computer or mobile device) is the "parent" device, and a second device is the "child" device. Incognito mode will only be disabled on the "child" device.
Family Link seems to work reasonably well, and I recommend it. IfIf you'd like to get started, you may set up a "parent" account now.
It has quirks
Google Family Link has some quirks. I've described the biggest quirk I've noticed, and its workaround, in another thread.
I hope that Google will work on eliminating the quirks in the future.
Despite its quirks, Family Link works reasonably well already, and I think it's a good way to disable incognito mode.
It may be easy to defeat
I'm not sure whether or not Family Link is easy for crafty children to defeat. But, in general, there are ways to defeat most parental-control software tools.
It's wise to buy your kids a flip phone with no data plan, and a non-portable computer which is permanently stored in a public room such as the living room. It's also wise to store all of your personal cellphones, laptops, and tablets in your bedroom at night, so that your kids can't secretly use them.