I've tested it briefly with Night Shift and F.lux and could see flicker, especially on lower brightness settings, but I'll try to catch it again on the video. Basically what F.Lux / Nightshift does is adding a little amount of red color to the tone (or removing amount of blue, which gives similar output), and it results in making red pixels brighter. In case red component is already there, it might be fine (as I couldn't see flicker on higher brightness of pixels), but if only blue / green subpixels are used, it can add more flicker as it will probably activate red subpixel in low brightness (which seems to equal additional flicker). I'll check different color profiles, I'd guess, if "Color LCD" is tuned for this particular display, they should add more flicker due to missing sweet spots.
The problem with observing whole pixels instead of just subpixels is that it's harder to see the flickering - three subpixels at once are brighter than individual ones which somehow misleads camera. You can check it on the second part of my video where I browse a webpage - there is some flicker, but it's not as noticeable as this on isolated "red" examples. It would be great if someone had better equipment, maybe then we could see the flicker on higher brightness and also observe whole pixels without issues.
Thanks for your comments guys, many useful ideas, just need to find time to test everything properly