This is an interesting question. I'm not sure if I've ever trained with anyone who has only one kidney. Having only one kidney is not something that could be easily recognized. My opinion (!) is that having only one kidney would in no way affect your ability to train in Aikido. I say this because the kidney is not involved (at least not directly) with any bodily system which you would use during Aikido training.
Kidney belts, like those used in motorcycle racing, are designed to prevent the kidneys from "bouncing around" during harsh landings after jumps (motocross or off-road racing). I suppose the belt may help prevent unnecessary shifting of the kidneys during a hard breakfall, but the belt may actually be a hindrance during ordinary rolling due to loss of flexibility in your lower back.
My suggestion is to give Aikido a try. If you find that certain aspects of the training are difficult, then perhaps your Sensei can make some allowances. I've trained with students who had prosthetic arms and legs. Certain techniques required some slight modification for them to perform, but they could perform them (quite well actually).
These are only my suggestions/opinions and are in no way based on medical fact, as always you should ask your doctor if he/she feels that the rolling and falling you will experience in Aikido could potentially cause you harm.
Have a good day!