Your father-in-law should feel better with the increase in kidney function. I have never heard of this condition where there are no major, native arteries below the knees. I say this not trying to be smug or act like I should have heard about it. It's just that I have done so much research on poor circulation in the legs, because mine is bad also, due to small vessel disease.
The collaterial arteries have kept the tissue of his legs supplied to some degree, because he would have developed gangrene. I would suspect that it is going to be painful for him to walk for any distances, but if he is otherwise able, he should get as much exercise for his legs as he can stand. A stationary bike would be really good exercise for this condition, as long as someone is always with him while he exercises. This will help to promote new collateral artery growth.
His age will limit his rehabilitation to some extent, as you know. He needs to make sure that he stays on a strict diet to help his kidneys. Limiting the sodium and protein would seem to be right, but check with his doctors on this, and any planned exercise program. He needs the best nutrition that he can get. Is there a rehabilitation program that he can start? His attitude and/or outlook needs to be at it's best. He needs a lot of encouragement and support from his family and friends.
As far as what this loss of blood circulation feels like, or causes, I can relate with that. His pain and sensations are probably a lot worse than I have felt. The calf muscles just more or less "lock up" in a constant type of cramp (claudication), whenever he pushes it, or tries to walk uphill. The loss of proper blood flow and circulation has more than likely damaged the nerves, or the nerve endings, of the muscles in his legs. This can cause peripheral neuropathy, which I have. It causes these wierd pains that constantly change, sometimes in a cyclical rhythm. Burning, numb, and tingling sensations can go up and down the chin, calves, ankles and feet. His feet can become numb and he can injure them without being aware of it. Many diabetics have to constantly check their feet. Ulcers can form and lead to infection and subsequent amputation. He should never wear any tight or uncomfortable shoes.
There is a medicine that I take that has helped myself and many with the symptoms of peripheral neuropathy. It is neurontin. It was originally developed as an anti-seizure drug, but has since been prescribed for PN and other ailments.
He should see a neurologist, if he has the symptoms of PN. Not that they can really help him, but that is their area of expertise.
I assume it was a vascular surgeon that said there was nothing more that they could do to help him. Do you really believe the doctor? If not, get him to see another doctor for a second opinion.
I really hope that he can recover and enjoy the rest of his time