Has anyone here ever gotten too close to a flame and had their eyebrows or other body hair singed off? You feel warmth, but it's too quick to cause pain or physical damage other than burn the hair off. That's how the flame clipping is supposed to work. Done correctly it should be easier and less painfull/irritating than electric clipping-you have to get all around the udder at closer range and can nick the skin, which could get infected... The problem I see with this is for one the use of dairy cows to begin with, and two, not being careful to do this correctly. As they said, the udder is valuable and you don't want someone who consistantly damages the udder, so there is incentive to do it correctly. Of all the husbandry practices, I'd say this is one of the better ones.
The hair is removed mainly for sanitary reasons. It can also interfere with the milking machine.