I translated this as "they need how many coats? but thinking about it, that is a clarification question. Possibly surprise? So that would be more like "hả? Họ cần bao nhiêu áo khoác?" or "Họ cần bao nhiêu áo khoác, à?" right?
Unlike the English sentence (which indicates a bit of a surprise), the Vietnamese sentence sounds natural. Additionally, depending on the context, your sentence "hả? Họ cần bao nhiêu áo khoác?" is acceptable, giving that one is surprised and trying to re-affirm the amount of coats. But, "Họ cần bao nhiêu áo khoác, à?" is not correct. "à" is equivalent to "right?" at the end of the sentence. Similarly, saying "you need how many coats, right?" does not sound right.
I feel bao nhiêu should be reserved for unaccountable nouns? bao nhiêu tiền? bao nhiêu cafe? For countable nouns, we should use mấy. Họ cần mấy áo khoác?
Actually bao nhiêu and mấy are the same but in countable we usually add cái next to the bao nhiêu (this is the different)