Arms are not used for kicks. Arms are used for blocking and striking. When you kick, the body above the waist does not move until you pivot and roll the hips. You do not swing, wave, or flap the arms; they stay in a tight guard position, even when performing a spin kick. Doing a fast, high kick does no good, if the opponent steps inside the kick and punches or kicks your unguarded face or body.
Kick similar to the way a duck swims. When you see a duck moving around a lake, the duck is moving calmly and smoothly through the water with its wings tucked with no apparent body movement. However, just beneath the surface, the ducks legs are thrashing like crazy.
Pivot on the ball of your standing foot as you kick to prevent ligament injury and to use the power generated by the rotating hips. For most kicks, the standing foot will pivot 180 degrees so its toes point directly away from the target. As the kicking leg is re-cocked, pivot the standing foot back to its starting position.