However, I don't get the problem when I'm using sunlight through the kitchen window. It seems to only happen when the lights in the kitchen are on.
Hmmm. What kind of lights?
This now makes me wonder about your shutter speed. If it is set to 1/60 or higher, try 1/50 or even 1/40.
Edit: Never mind. This doesn't really flicker that much. But, I still wonder about the lights. This is odd...
Shutterspeed is a 1/50th, shooting 1080p, 24fps.
No clue what kind of lights they are unfortunately, all I know is that they're fluorescent tubes. More disorientating than any other fluorescent lights I've seen though. They were recommended by the builder when we were getting the kitchen done up, we asked for powerful lights as our kitchen gets a lot of use for multiple things and we usually have dark days 95% of the time here in Ireland (doesn't help that the sun is on the front of the house and not the back where the kitchen is), so he said these were the most powerful he'd be able to put in.
I unfortunately can't remove the cover to check for a name/brand or anything.