Dark clips keep flickering like a VHS-tape

Could the flickering that you see also be described as a shimmering, or speckling, plus the lines?

Although the footage doesn’t seem to exhibit what would typically be called “flickering,” there is a noticeable amount of noise in it. If I’m seeing what you are, it’s constantly shifting clouds of digital noise that are primarily in the shadows. Those, and the lines, are to be expected if a digital image (in a still or video camera) was exposed at a high ISO setting. And that would happen if the camera was either set to a high ISO setting manually, or if the ISO setting was set to automatic when the light level is very low.

Good cameras can shoot relatively clean footage at a high ISO setting, but lower quality cameras are noisy at high ISO settings and can look a lot like this. Even a good camera will be noisy if the ISO setting is pushed too high. Professional video productions avoid high ISO noise by adding a lot of light, so that a clean low ISO setting can be used. Lighting scenes properly is probably the solution to this problem.

There may be an explanation for not seeing it on the camera display. It may have been harder to see on a small screen, and if the camera screen was set to a different brightness (especially lower), it would have been much harder to notice. This type of noise is usually easier to see on a display set to a high brightness level, or when the shadows have been boosted too much.

There is not much you can do after it’s already been shot. You can try adjusting the black level and shadow levels, and make sure the computer display you are using is at the correct brightness, especially making sure it isn’t brighter than it’s supposed to be for editing. It might be possible to use a noise reduction plug-in to smooth out the noise, but this may require a more powerful computer and make render times longer.

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When we shot it, there was no flickering in the camera display

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That implies you were there when it was shot. Do you know what camera it was ??  More especially, do you know how much the ISO was cranked up to shoot at night with one light ????  Was it like around 16,000 ISO ??

I think you just basically shot with a junk camera for that and the chip ( and it's ability to process the image from the chip to the media recording thing ( SD card ?? )) was totally stressed out.

Please use the free MediaInfo and post a screenshot the properties of your media in tree view:
https://mediaarea.net/en/MediaInfo

I see the lines on the still but not in the video.

Post screenshot mediainfo of original footage and screenshot export settings.

There's no any flickering. If you are working on a monitor with HDMI try changing that cable for a better one. 

I saw no flickering on your example video. Maybe it's your video card or monitor. Try updating your video card driver from the manufacturer; or, changing the refresh rate of your monitor. Just a thought.

Can you post a sample of it?