Hi Monroe.
I cannot speak for the kidneys, but as for the gout, my Bf has it and he does Atkins. He has been doing Atkins for 6 months.
First I suggest he get a new Doctor.
(Really)
They make medication to control his uric acid. It's Allpurinol.
You should take a look at the foods high in uric acid, which are what trigger Gout attacks. These are pretty much organ meats, seafood and dried beans. Shell fish is a main triggering food. (also any alcohol consumption)
The Gout attacks can also be triggered by high cholesterol & high blood pressure.
My BF got attacks all the time when we first sent on Atkins, and now with a small dose of Allpurinol he has had no attacks for several months.
As long as he is under a doctors care, they should be glad that he is trying to better his health, whether it be Atkins or any other form of dietary change. Good luck!!
I know you'll both do well!!