I'm not sure why anyone would want to eat menstrual flow.
You would become seriously ill as menstrual flow contains a lot of bacteria, also blood is toxic to humans - we can't process the iron in the blood, it can make you very ill or even be fatal if you can consume enough without throwing-up. Obviously if a person has an STD then you'd be at risk too, particularly blood borne STD's such as HIV. There have been cases of disgruntled workers using their used tampons in employers food to try to pass on HIV via their menstrual blood.
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Well, what happens is you will have these weird delusions that you are a zombie. That's naturally what the body does when you eat your own period blood. This will happen because period blood really is not' blood it is amniotic fluid from your eggs that come off as red. You will probably get extreme growth in your pubic hair area as well. Once this happens you need to drink a lot of vitamin c or about ten emergence's. If swelling appears in your mouth, genitals, or feet consult a doctor immediately.
Absolutely nothing happens if you drink on your period - you can do anything during menstruation that you would do normally.