Each of Kairos' heads is an accomplished Level 4 Wizard. They do not roll randomly for spells. The left head may choose any four spells from the Lore of Life, Metal, Light and Heavens. The right head may choose any four spells from the Lore of Death, Beasts, Shadow and Fire. Both heads always know all the spells from the Daemon Lore of Tzeentch.
At the start of each Magic phase, decide which head Kairos will use. He may only cast spells known to that head during the phase. Kairos generates the Power and Dispel dice for one Level 4 Wizard, not two.