They are weaker than a nightmare. 'Their magic attack is stronger' only means that their casting abilities are stronger when directly compared to a nightmare. But that even ignores the fire breath of the nightmare. Not to mention that the difference when fully trained shrinks to the kirin having more int.
There is no 'special chain lightning attack' with a kirin. I have seen it in the past and it was never really usefull. The message when this happens is something like: 'Your kirin calls down the force of nature upon your opponent.' The special about that is, that your kirin used that while you are riding on it. I am not fully shure about it, but i would say that it has the same limititions as the cure from a unicorn. (While the kirin calls the forces of nature, the unicorn can cure its rider. Both creatures came out at the same time ... one for male tamers, the other one for female ones.) Both creatures can use their special when their riders drop in health. (If i remember right it was around 30%. So if your health drops below 30%, your kirin can call the forces of nature while your unicorn can cure you, if your poisoned.)