It was not based on the law

"His becoming priest was not based on the law"

the law of fleshly descent

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