When should you see a doctor for kidney pain? how severe / persistent does the pain need to be?

Soon: don't wait if the pain is worrisome get it checked an untreated UTI or kidney stone may end up causing kidney damage

Kidney Pain?: I would like to ask what you mean by "kidney pain". Quite often, disease involving kidneys are not associated with symptoms. If you mean having low back pain, it may not be related to your kidneys unless there are other associated symptoms such as blood or odor in the urine. I do encourage you to see a primary care physician. Hope you feel better soon.

Flank Pain: Most of our organs do not have pain receptors but we feel what is called "referred pain". For the kidneys, which are retroperitoneal organs (behind the peritoneal lining) we feel pain in our flank in the case of a kidney infection or stone in the kidney or ureter. A doctor will "knock" on your flank. It sometimes MD's like you are having symptoms of pain in your back/flank and should see a doctor.