Kinetic energy is not zero in any state of matter. Kinetic energy arises due to the movement of molecules.When the state of matter changes the corresponding kinetic energy also changes as the molecules either slow down (gas to solid) or move faster (solid to gas). In the liquid and gas state, molecules are in motion, thus they posses kinetic energy. Solids possess negligible kinetic energy (but non-zero) as in solids the molecules are arranged compactly and they can only vibrate.