I think there is not a direct way to do it from Mendix Studio as it always open the application in a normal window. So if you want to test your application in incognito you can copy the url, open an incognito window on your browser and paste the url there. With that you'll be able to test your application there.
Do you want to see the app in incognito when you click on view app ??
What we do is - we know the url of the application.. open incognito mode and then we paste the url.. application works fine.