I typically do a hard flat first serve and then a slice second serve, but I'm curious to know the fundamentals behind adding "kick" to a serve for higher bounce.
The following is a rough, elementary answer. It disregards subtleties such as pronation which are relevant to high level play.
The fundamental mechanic behind a tennis serve is that of throwing a ball. In a basic flat serve, your motion is that of throwing a ball forward. In a kick serve, the motion (for a right-handed player) is of throwing a ball to the right. This is usually enough to force the racquet to hit the ball upwards, generating the desired spin.