I want to know if CoolSculpting would damage my kidney through the fat elimination process?

This is a great question. Actually, the good new is that CoolSculpting will have no effects on the kidneys, as the dead cells will be filtered out by the liver. And, even though the fat cells will be removed by the liver, it happens at such a slow rate over a period of months, that no damage is possible to the liver as well. CoolSculpting is a remarkably safe and effective way to permanently remove fat cells from the body. Good luck with everything!

There has never been shown to have any adverse effect on kidney function, with Coolsculpting. You should be "good to go!" :)