Light flicker is sometimes a struggle for us as well. Here's some solutions for overcoming it:

1. Use a camera with manual features. With a manual camera, you can adjust the white balance, shutter speed, exposure and f-stop. Without these features, your camera will try to auto correct each frame which will result in flicker.

2. Put paper on your lamps. While some advanced cameras may not need diffused lighting, most cameras do. Putting paper on your lamps helps to reduce the hardness of the light and puts less stress on your camera.

3. Try to have consistent light. This means that the only light that should be on your set is the light coming from your lamps. Outdoor lighting, people moving, ceiling lamps, etc. can all cause light flicker, due to it causing shadows and the light being uneven. Having the light from only one source prevents these problems. It is also best to film at night, and if you do have to film during the day, then make sure to blackout any windows around you.

Hopefully this helps you out. Light flicker is a common problem in brickfilming, so it's no individual sort of problem.

It's difficult to get rid of flicker in post-production, from my experiences. I have tried to do it numerous times and have failed at every attempt. Your best bet would be to re-film that specific shot if it is really bugging you.

Only if you use incandescent bulbs.
On topic, I have found that it sometimes works to go through frame by frame and fix the ones that need it, individually. However, this is a pain. Apart from this, I don't know how else.

2nd place Darkness and Light entry: The Tree
Behind the Scenes

You might have to experience with numerous different filters. Brightness, contrast, saturation, color balance, etc. This can be done in most photo editing programs.

What JP said. I know it's possible in gimp (if that's what you use). I tend to use after effects, as all the frames are right there together and I can compare them easily. But idk what programs you have.

2nd place Darkness and Light entry: The Tree
Behind the Scenes

In the films "Besita" a virtualdub plugin called MSU deflicker was used (it was originally made for time lapse videos)