Beyond what others have commented, blood cells (white blood cells included) don’t actually undergo mitosis in the blood stream and make other blood cells. They all die within a few weeks.
That said, since blood is created in the bone marrow, if you have leukemia and got a bone marrow transplant then those white blood cells this new bone marrow produces *would* contain the donor DNA. It still wouldn’t change your DNA, but your blood would be carrying foreign DNA. If you then committed a crime, if you left blood then it might match the donor, but if you left hair or skin, it’d match you.
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