What is the minimum height of a chimney?

Well I have never heard of a minimum height,but your local building inspector would have a code book or local ordinance for the required height above the roof peak.

KBC

A chimney must be 2' taller than the highest part of the roof within 10' of the chimeny. If you have a totally flat roof this would be 2'

That is true, but the higher the better, and it depends on the direction the wind blows from