"I've learned that kidney problems may be the cause of high BP"
They can, but most people with high blood pressure never actually find the cause. It's simply put down to some people having this condition. It is also known that as we age, our arteries become less supple and our blood pressure increases which is why most elderly people end up on medication to lower it.
"but has never mentioned kidney tests"
Neither have my kidneys ever been tested. When I questioned my Doctor about this, she said that if my Kidneys were the problem, they would certainly be giving other symptoms, not simply raising blood pressure. The list of kidney problems include...
Urinating a lot through the night, Pale skin that bruises easily, weakness tiredness or fatigue, Itchy skin which progressively gets worse, muscle twitches/pains/cramps, pins and needles in hand/feet, feeling nauseous and loss of appetite, swelling of face hands legs and abdomen. The list actually goes on much further so I think your Doctor, as mine, is keeping an eye out for other symptoms which don't exist. Suffice it to say when you get kidney problems it's usually pretty obvious.
I've had high blood pressure since a kid, and only in the last three years have they decided to do something about it (49 years old now).
If you have been seeing a doctor for many years, it would be proper protocol to have had a blood test.
But specific tests is a urine test. Healthy kidneys leave proteins in your blood but if you have kidney disease there might be traces of a protein called albumin in your urine. There is blood test to determine waste your blood. The waste product is creatine.
Take a Blood Urea Nitrogen test. This test requires only a small blood sample and will tell you how well your kidneys are functioning.