That isn't a chemical reaction, but a physical one.

The detergent destroys the surface tension in the middle of the liquid, which is what causes the outside of the milk to appear to "suck" the colouring to the outside of the dish.

It also weakens the forces between molecules wherever it goes within the liquid, so that the liquid has uneven distributions of inter-molecular force, causing the swirls and eddies seen in the video.

The viscosity and opacity of the milk contribute to slowing down the flow of liquid and making for a spectacular show. :)

It probably isn't a great idea to go to sleep with earbuds in or this headband. Extended exposure to an auditory stimulus like this is almost certain to cause hearing damage. I'm living proof: I used to go to sleep almost every night with headphones on (not even earbuds, which are even worse for you) and within a few years a routine check-up revealed a permanent 15% loss of hearing in both ears, across all frequencies.

I never attended rock concerts or had loud music playing - so this is the only major risk factor to which my hearing loss can be attributed, I'm afraid.

Excruciatingly forced iambic pentameter :(