No, you can live perfectly well on only one kidney and there should be no ill effects from this at all.
Has he always had one kidney or has he had one removed due to infection? If he has had one removed, then the other kidney should enlarge slightly to take over the work of the other one. He will need to have regular check ups though to ensure that the one kidney is functioning well and he should ensure that he drinks plenty of water and not become dehydrated. Other than that, there should be no effects at all of only having one kidney. I have to say that the sunburn is just a myth, as tanning and burning are to do more with the sensitivity of the skin rather than the kidneys.