Screen brightness flashing (turning brighter to dark and back again) randomly while playing some video (youtube, dailymotion etc.)

This always irked me when the auto-brightness "feature" was first added to the Mac portables: even if a moth flittered in front of the sensor would cause screen brightness to start jumping. Which is why I have that disabled everywhere, Macs, tablets, phones (Settings / Display & Brightness / Auto-Brightness).

In your case, the fact that the room is dark implies the light from the screen, which varies as the video progresses, is bouncing off your face/clothes/surroundings back to the iPad's ambient light sensor and creating a feedback loop.