How does milk stop your mouth from burning after spicy food?

Milk coats the mouth, even your throat and stomach so it helps with all

The Capsaicin in the food docks with your taste receptors on the tongue, giving you the burning sensation.
Capsaicin however is soluble in milk, or more specifically, the fat in the milk. It removes the capsaicin from the receptors and binds it.
And no, milk does not coat the tongue.

Do you think it would be possible to make something that goes into yor food to make it less spicy? hopefully without making a big difference to the taste

No.

According to chefs who cook with spices a lot, use sugary ingredients like fruits, honey etc. And that somehow balances things out.

Ive also found that long cooking dissipates the heat somewhat.

And whatever types of chili’s you use, before dicing take out the seeds and the ribs (the white membranes) cuz thats where most of the heat is contained.

But there is no magic ingredient, per se, that you can add as a magic cure all. The obvious answer is to use. LESS of the hot ingredients.

I don’t even use pepper when I cook (and neither does Chef Anne Burrell)

It never worked for me. But drinking vinegar seemed to help. I don’t know if it was because it just pickled the inside of my mouth temporarily or whether it did something to dissolve and wash out the capsaicin… it worked.

@inunsure You may have noticed that starchy Mexican food isn’t as spicy as the spices on their own. Rice, tortillas, and bread are all mitigators.

@inunsure Everyone I know adds a bit of salt, if it’s too spicy.

WRT OP, @ragingloli is correct.

Avocado, cheese, and other fatty foods will have a dissolving affect similar to milk.

Baking soda and water also heal burnt mouths do to foods

When cooking with spices you can use less chilli and still retain the spiciness of the other flavours without so much heat.

As mentioned before multiple times, serving a spicy dish with a side of something starchy or bready like rice, bread, or tortillas will help make them easier to eat, but fat can control how much it burns and for how long.

Curries for example vary in intensity depending on the amount of fat in them. Milder curries like korma and Tikka masala gravies are pretty mild because they both use yogurt compared to the agressive ones like vindaloo that don’t have any fat to mitigate the heat in the spices and chilies. Thai food does the same with coconut milk in their curries.