The final element of the kick serve is the follow through. Because you were swinging in a different direction prior to and at contact, you’ll follow through in a different direction. The rest of the mechanics of the follow through are the same: all your weight ends up on you front foot, your racket head points down at the court during your follow through and you bring the racket around to the other side of your body.
In the video we compare Oliver Akli’s follow throughs on his kick serve and flat serve. Because Oliver swung up and across the ball on his kick serve, he is going to follow through more to his side. It looks like his arm is moving toward the camera as opposed to into the court on his flat serve. You will end up with some space in between your arm and the side of your body.