How serious are someone's chances of getting graft vs. Host disease if I get a donated kidney?

Very small. It is very rare to develop gvhd with a kidney transplant . It is more common with bone marrow transplant and intestinal /multivisceral transplantation.
No. Almost no chance, unless donor bone marrow was also transplanted with the kidney intentionally. Graft v host disease more commonly occurs in bone marrow, pancreas, or liver transplants, because lymphatic tissue is often transferred from the donor to the recipient with the transplant .