You won't gain anything by sending it through the mill, but it won't hurt anything either.
You can gum up your mill.
Really? Maybe if it's damp or you mill gap is insanely right, but it should just go straight through.
My mill gap is definitely insanely right.
I've milled flaked grains before, but not on purpose. Everything tends to get mixed together when I weigh out my grains. I certainly haven't seen any harm come from it.