How do you increase explosive power in your clap push-ups? The goal isn't to do more of them or to build larger chest / arm muscles, but to launch oneself higher off the ground.
There are 4 types of muscular development:
Developing strength won't help the clap push-up, because you usually want to do more than one push up. Building mass doesn't help you get height on the push-up because the more massive you are, the more force gravity pushes you down (force = mass * gravity).
You will need to develop cardiovascular endurance to sustain you through a set of push-ups. The push up is a compound exercise, involving pecs, triceps, anterior deltoids, and core stability, which is a lot of muscles that are gasping for oxygen. To gain explosive power of the clap push-up, you obviously want to develop your power. Power training will propel you to new heights, literally.
The following chart will show you how to build endurance and power. Since push-ups are dependent on body weight, you won't be able to easily tune the load and rep range into the endurance and power zone. So I recommend using free weights for total control. You can do dumbbell bench presses, barbell bench presses, and dumbbell flies to develop chest power and endurance. Preferably, do these exercises on a flat bench to mimic the position of a clap push-up. However, the part of the clap push-up before your hands leave the ground does slightly resemble a decline press, so incorporate declines as well.
Ross Enamait provides a very good video tutorial on the triple clap pushup - something I have yet to achieve.
A great plyometric exercise that I'm looking into to help with the bottom part of the bench press.