What is the EVOLUTIONARY ADVANTAGE...

of periods?

Is it an adaptation to flush out the vagina of foreign material (bacteria, debris, etc.) ?

Appears so.

And clear the dead egg (s)

Ummm... no.

The "blood" is just uterine lining that was all ready for a baby that never happened. After a while of waiting for a fertilized egg, it gives up and leaves.

The evolutionary advantage being that the body doesn't constantly have to maintain that state of readiness. It takes less energy. Hormones CYCLE, instead of constant full blown PMS (in-heat for animals, PMS for people)... which is what would otherwise be the case.

Hormones CYCLE, instead of constant full blown PMS
Ah, of course. So periods are a survival mechanism. Without them, the entire population would be driven to extinction. Consensual mating would cease entirely and the males would all either be killed off in horrible confrontations or would be driven to mass suicide.