I asked my daughter to menstruate on the flag so that it's red like the flag of China
That sounds quite vile and odd. I'd never want something like that to happen!
I wanted the flag to represent the pain of my family.
Aside from the desecration of a flag, that was a creepy request to make of you child. That is not okay to ask of her.
Well, I'm the dad here. We should wear all sorts of stuff to express ourselves, it it's not hurting anyone.
It could definitely make your daughter feel uncomfortable if you want such weird requests. Why not just try to paint a flag together instead? It could be a fun activity for the family.