Well that silly question got your attention... Kosher means fit or proper.
Yes, you will know that menstruation is kosher, if you are an educated person. There is nothing unfit about it. It is a normal part of human health and life.
But according to an op-ed report in the Times, "The Taboo of Menstruation," religious and cultural taboos concerning menstruation are widespread in India, to the degree that, "The taboo of menstruation in India causes real harm. Women in some tribes are forced to live in a cowshed throughout their periods. There are health issues, like infections caused by using dirty rags, and horror stories..."
Menstrual taboos also exist among Orthodox Jews, though to the best of our knowledge without the concomitant damaging physical health issues. We are not expert enough to comment on whether there are damaging psychological or social issues associated with the taboos. We were taught about only the beautiful meanings of the taboos when we studied at the Orthodox men's schools of Yeshiva University.
The Talmud has a tractate dedicated to the taboos: in English translation - Niddah (The Menstruant: 10 chapters, 73 folios, 509 pages) Nidah.PDF and in an improved edition 52a Niddoh 2a-23a | 52b Niddoh 23b-48a | 52c Niddoh 48b-73a, and a Kindle edition, Soncino Babylonian Talmud Niddah (Soncino Bablylonian Talmud).
Talmudic Conclusion: We don't like any taboos that are damaging, especially those directed by men against women.