What is causing these horizontal lines moving vertically up the whiter portions of the video?
You seem to have a flickering light source that is out of sync with the camera's rolling shutter.
Traditional lights
You should first verify that you are filming in 60/30/24 fps in regions whose power grid uses a 60 Hz frequency, or in 25/50 fps for 50 Hz.
If that is impossible to achieve, you can also adapt your shutter speed or angle to be a multiple of the utility frequency. Red provides a nice calculator for this.
LED lights
Flickering can be particularly bad if you use low quality LEDs because their flicker index (or depth of modulation) can be worse than conventional light sources.
They might also flicker independently of the utility frequency. This is especially true for RGB lights or when dimming.
If you can, choose good quality high frequency switching or flicker free LED drivers, or ones that are made for video. You shouldn't have any flicker problems with good LEDs. You can also try to disable dimming or setting the highest power output to reduce flicker.