Of course, what your arms are doing is only half the story. There are a lot of drills you can do to improve your kick.
To improve and strengthen your kick, lie on your side, with your bottom arm extended above your head, and your head resting against your arm. Your bottom hand should be about eight inches (20.3 centimeters) below the surface of the water. You top arm should rest on your hip. Concentrating on pushing your bottom armpit toward the bottom of the pool; that will force you to push your hip up, and keep your core engaged. Perform your scissor kick on your side like this for a few laps, then switch.
You can also improve your kick by giving your arms a break. You can with rest your arms on a kickboard or extend them out in front of your head, turning your head occasionally to breath.
While swimming is mostly equipment-free, using flippers specifically designed for fitness swimming or swim training can improve your kick. The flippers will force you to keep your legs fluid and loose, and keep you from locking your knees and ankles.
Another drill you can do involves counting your kick. In these drills, each kick counts as a beat. In a six-beat drill, you'll want to perform six kicks for each arm stroke. As you kick, focus on rotating your trunk from your hips for each stroke. Like arm drills, you can improve your kick by playing with the rhythm. Try alternating kicking and stroking. Or, do two kicks, then a stroke. Breaking up your motions allows you to concentrate on each movement individually.