I'm not sure what brown flour is - at least where I live in the US that is not something I've ever even heard of before.
I know that our whole wheat flour is sometimes bleached. This doesn't change the color (much?), but it kills a number of nasties and thus makes raw flour safer. (you should still never eat raw flour, but if you do bleached is safer... I know many people do eat raw flour, but there are some things can can hurt/kill you if it isn't cooked). I'm not sure if whole wheat is what you mean by brown flour or not.
Flour is used to make food not stick to cooking and preparation surfaces, therefore lots of raw flour is eaten intentionally on the outside of baked goods (bread, pizzas etc).
Baking has been a major hobby for 15 years. I know the dangers of raw egg and flour but licking the bowl/beaters/spoons is still a major highlight of many of my recipes. And, of course, there's always raw cookie dough.
Maybe not the smartest choice for longevity and health, but yes, eating raw flour is totally a thing!