I have raw video with horizontal lines (bad settings at manual mode); here's a preview: http://sendvid.com/oh3uxjqi
Can I remove this using some software, or effect/plugin in Premiere Pro?
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I think the other thing wrecking your video is that your source is interlaced but you are processing as if not interlaced. Interlaced video is an anachronism from the days of analog. Digital camcorders can still record 1080i, but that leads to very unhappy images when presented on non-CRT screens. If you don't know what a CRT screen is, you should definitely change your settings to shoot progressive instead of analog. (And if you do know, you can easily understand why you should shoot progressive anyway.)
Moreover, a progressive format like 720p24, 720p25, or 720p30 (or 1080p24, 1080p25 or 1080p30) will slow down your shutter speed, which will also reduce whatever flickering effect might exist as mentioned by others.
Premiere Pro does have a "de-interlace" filter, but it's difficult to repair the damage of interlacing. Best to shoot progressive from the get-go.
How I understand you speaking about illumination flickering.
It looks like artifact from different fps and light bulb flickering.
Usually you can fix it like that:
That shall compensate flickering.