It was not based on a law

"His becoming priest was not based on a law"

a law of fleshly requirement

The idea of human descent is spoken of as if it had only to do with the flesh of one's body. Alternate translation: "a law of human descent" or "a law that required priests to be descendants of priests" (See: rc://en/ta/man/translate/figs-metonymy and rc://en/ta/man/translate/figs-explicit)