8 fl oz of flour spooned into the measuring cup or 4.5 oz. by weight.
I'm not at all trying to be snarky here. Like any other specialization people who cook have organic terminology that is useful to the in-group but confusing to the out-group. A /24 isn't the same as a class C network but we all know what is being conveyed.
And you'll get much more accurate measurements of small quantities measuring by volume instead of weight since kitchen scales aren't that accurate. Knowing that 0.25 tsp is about a gram for just about any granular thing will probably do better than your scale.
It also helps convey the sig figs in recipe. Very few recipes have a tolerance of 1 g. Even finicky bread doesn't get that accurate so it's ridiculous when some bloggers write something like 113 g when without question the recipe was originally formulated to be 4.0 oz and you just messed up the conveyed tolerances by blindly converting.
Most of the time when I'm cooking and I see an American recipe I just google the conversion; a cup of milk is easy to deal with. Just a minor irritation most of the time, but for some things it matters.
Maybe I've watched too many infomercials and soaps. I've reached a point where I know Americans don't have (electric) kettles, but a scale seems like a necessity for anybody who cooks.
(I guess there are lot of people, American, or otherwise, who just don't cook. So I'd understand in that case. But cooking without a scale just seems surprising. Even where I come from a grew up with a balance-scale with brass weights. Never hugely accurate, but always available.)
What is one "cup" of flour? It obviously depends on how fine the flour is. Use grams! Use ounces! But above all use some kind of real measurement!