What is the ds id code for Mario Kart?

Not sure exactly what you mean here, but it might be that you want to find you friend code on Mario Kart Wii. Here's how:

From the main menu, choose Nintendo WFC. Then choose Friends. Then it will display your user name and me at the bottom of the screen along with a 12 digit number separated by two dashes. This is your friend code.

Hope that helps.