I am not an expert, but what I have the same issue, and I think I understand it. If you live in the United States the AC current coming out of your wall oscillates at 60Hz. This means every second your electricity is going back ad forth 60 times every second. This causes your light to flicker on and off 60 times every second. Your eye, and normal cameras, do not see this because it is to quick to notice. But, a camera that is filming at 240 frames per second is taking a picture more frequently than the light is flickering on and off. So, you see the light flicker in your video. To prevent this, you have to use a light source that uses DC current, such as a flashlight or an LED.
To better see this effect, try recording a computer screen in slow motion where you can see the reflection of a regular light on the screen. You will see that the computer screen does not flicker because it has DC power. However, the reflection of the normal light will flicker.
I am not 100% sure that this is fully correct, but it is the best explanation I can think of.