Did any of Mary's blood flow through Jesus?
No. According to the explanation given, the major components of a mother's blood never pass through the placenta to the fetus, and none of Mary's blood coursed through the baby Jesus. His blood system came from His Father, just as any child's blood system comes from the father.
Les teaches that a physiology book used the analogy of fencing a garden: netting keeps out rabbits and dogs, but insects and smaller mice still get through. Similarly, the placenta prevents the major components of the mother's blood from reaching the fetus, though small chromosomes and genes carrying inherited characteristics do pass through. So when Mary was the physical fleshly mother of the Lord Jesus, none of Mary's blood—which was just as corrupt as any other woman's, since she was a sinner too—coursed through the baby Jesus. That is not how physiology works. Instead, His blood system came from His Father, just as any other child's blood system comes from the father. Les notes this boggles many minds, and he ties it back to the promise of the seed of the woman in Genesis 3:15, then Matthew 1 introduces the New Testament with similar language: the book of the generation of Jesus Christ, the Son of David, the Son of Abraham.