Clones are made by transferring the nucleus of an adult cell into an ovum, and then getting the ovum to replicate. That means that unless the donor ovum came from a maternal relative of the nucleus donor, the resultant clone would have different mitochondrial DNA from the original.
Now, I have no idea what role mitochondria plays in organ rejection, but if your goal in having yourself cloned is to have a reserve of organs, I suggest you play it safe and get a maternal relative to donate the ovum. Or do it yourself, if you are female.
On the other hand, an awful lot of kidney transplants happen for genetic diseases, so you might not want the kidney of a clone. They do happen for other reasons, such as a disease that started out as an infection, but if your genes dictate a lifespan for your kidneys of only 20 years, you’re gonna need a lot of clones, and they’re gonna have to be fine with dialysis or waiting for a cadaver kidney.
Livers fail because of hepatitis, much of the time, and that’s an infection that your clone can avoid, after giving you a donation.
Lung transplants happen a lot of the time because of genetic illnesses, like certain forms of cystic fibrosis. People who lose a lung to cancer after smoking don’t usually get on the donor list, because they first of all have to be cancer-free for a certain amount of time, and they also have to stop smoking. You would be shocked how many people undergoing treatment for emphysema, lung cancer, COPD, or who have lost a lung, or part of a lung, are still smoking. It’s mind-boggling, especially with alternate nicotine delivery systems. At any rate, if you want to smoke, and have a spare lung in your clone, you’re going to have to convince him not to smoke, the whole time you are doing it. Good luck with that.
All in all, clones may not be the best way to go. Yes, the organ will be a perfect, or near-perfect match, but in that, it may just bring with it all the problems of the original.