The kidney doctor is a great idea. My mother has had high blood pressure for decades, but a couple of years ago it went sky high. They couldn't get it down, and she ended up in the hospital where she was seen by a kidney specialist. He was able to prescribe medication that took it down and has kept it down lower than it's been in decades. A specific kidney problem was never diagnosed (although she found out she only has one working kidney and they said the other one had been useless for years and possibly her entire life - 70 years).
Generally, if we all live long enough we will most likely get hypertension. It is a result of decreasing compliace of the arterial wall as we age. Some will develop it before others, there are certain genetic factors involved in the process that are not well understood. There are some causes of secondary hypertension that are not from this process. It is not effective to screen all patients that have hypertension for these other causes unless there are clues to their existence. On of the most common clues is difficult to control blood pressure on multiple medications. The general rule is maximum doses of 3 medications. I usually start thinking about it though when I'm adding on a third.
I usually screen most patients with new onset hypertension for diabetes, kidney function and thyroid dysfuction. I'm not sure what kidney test your doctor is referring to, but it may be looking for renal artery stenosis. The kidney is an important organ in controlling blood pressure. If there is blockage in the artery that goes to the kidney, the kidney interprets this as needing to increase blood pressure to maintain its perfusion and secretes hormones that cause blood pressure to rise. Clues to the presence of RAS include elevated kidney function test, or a bruit(murmmer) hear on the abdominal exam.
I'm not sure what medications or doses your father is taking. The most common cause of someones blood pressure staying high however, is submaximal dosage of blood pressure medication. If your father is on more the 3 medications in MAXIMAL doses, he should be screened for other causes of hypertension.