Sorry for the delay.
I was checking this issue and trying to reproduce it but I was not able to do so. I have tested the same NUC model and tested different monitors with mini DP and HDMI but It did not fail.
At this point, I recommend you to update the BIOS In your system to latest. You can get it at this link:
You can also try uninstalling completely the current graphics driver and reinstalling it again from this link:
Testing different monitors or cables is another option.
As I said it only happens when the right-click menu contains the Intel graphics options, other right-click menus are okay.
If I uninstall the graphics driver, then every right click is working, so this is definitely a driver issue.
By the way I disabled the tray icon of the graphics driver and if I enable it, then sometimes the right-click menu is okay, but sometimes not and I can't figure it out when it happens, but if I hide the tray icon, then it always happens.
So maybe you can try disabling the tray icon and then check if this problem is happening.
There are other similar discussions about right click problems with the Intel graphics driver, but not here on the NUC section.
I removed the Intel right-click menu from the registry and now everything is working and there's no more flashing screen when I use the right click.
So it's a driver issue and it needs a fix, but if anyone runs into this with Windows 8.1, then you can delete the below entry from the registry to solve the problem.
If you use an older Windows, then try to delete the following entry: