^ Sounds more like a topspin serve, which can be generated by swinging up and to the right so as to brush up on the ball.
A kick serve can be done by brushing "around" the ball. The best analogy I was taught was to carve the ball like you're "peeling an orange". This emphasizes coming around the ball in order to achieve the right spin.
The next step is to work on the toss, which should, ideally, bounce just behind the shoulder of the arm that tosses the ball.
Honestly speaking, though, I abandoned my kick serve back in high school. I had/have a much better handle on my topspin serve, and I can actually be quite effective with it.
Il work on getting it to bounce to the side but I am happy with the high bounce . I already have a good topspin serve that,s very fast.