In which state of matter has the least kinetic energy

In solids.

In fact, when the substance is in solid state, the atoms (or molecules) are bound with each other, and they are not free to move, but only to vibrate. This means their kinetic energy is minimum. Viceversa, when the substance is in liquid or gas state, the molecules are not bound together and are free to move in the substance, so their kinetic energy is larger than when they are in the solid state.