An American invention, for the most part. You’ll see the occasional drizzle of thin crema, but typically not tacos piled with cheese in most states.
zoid:
Wouldn’t the soap do the trick just fine without using the oil first? Soap is made from fat, isn’t it? Whenever I eat buffalo wings, I just wash my hands with soap afterward, and after that, no problem touching my eyes or any spot that might burn.
(Obviously, the OP wouldn’t want to wash his mouth with soap, this is just a question about you and your hands.)
According to the Mythbusters the best cure is full-fat milk. Alcohol may also work but it comes with its own issues (you need something stronger than beer).
Soap contains amphiphilic fatty acids. These surfactants help dissolve fats and oils into water.
If you have the run of a kitchen, some reasonably chewy bread covered in butter and/or peanut butter would have been my recommendation.
In a mexican or indian restaurant you can usually source some type of flat bread (naan/chapati/tortilla). In thai or similar restaurants, sticky rice is good.
The chewing dislodges the stuff from your mouth and binds it up in the carbs, then you swallow it. Anything greasy/fatty to help is a bonus.
Nothing substitutes for a little caution when ordering and/or sampling, though. I’ve learned the hard way to be very cautious of small skinny dried-out looking chilli peppers and any sauce with visible seeds and/or very fine slices of pepper.
I agree, I tend to push the limits once in a while on how hot I can take something. Simply eating a tortilla or some other semi dry type food does seem to carry a large part of the burning substance away. I have had no luck with milk, beer, ice cream or water.
A WAG … vanilla is structurally very similar to capsaicin and should somewhat compete for the same receptors. (They are both vanilloids.)
I would think some true vanilla extract mixed into the butter on bread or peanut butter on bread would increase the efficacy significantly.
So the answer is: vanilla ice cream
No, a tequila ice cream float. 
Not sure why but plain old soap just doesn’t do it.
Ever had your hands covered with oil based paint? Soap and water don’t do a thing. “Wash” your hands for a few minutes with cooking oil and the paint comes right off.
Milk works to help get it out of your mouth. Stops the mouth burning, you’re still going to be lined up for a Johnny Cash song when it makes it’s reappearance at the other end though.
no doubt. I had a plate of chicken wings with the hottest sauce the place had (yes, I’m one of those guys.) Eating the things was fine. But the next day, Gott im Himmel my lower GI tract was threatening to rise up and slay me.