Yeah, it's a good question. Here's what I know. It's definitely not flightcrew, but that doesn't rule it out as a compound noun. If we agree it's a compound noun, then we are left with a choice between "flight crew" and "flight-crew". At this stage, you can usually let aesthetics guide you because our two-word compound nouns are in a massive state of flux. Some are transitioning to one word (eyeopener), some are transitioning to hyphenated words (ice-cream), and some are not (peace pipe). Some exist in all three versions (chatroom, chat-room, and chat room).
There is nothing to suggest that "flight crew" is a compound word. It's not; it's a syntactic construction (a noun phrase) with "crew" as head and the noun "flight" as attributive modifier.
Just because "flight crew" is a commonly used expression, i.e. with a semantic connection, that doesn't mean that syntactically it's a single word, because that is what compounds are - single words, just like "ashtray", "goldfish", "pillow-case", "bulldog" and the like.
Even if it were a compound word, the first element "flight" would still be a noun, as is the second element "crew". It would then be a noun-centred compound noun.
It's no different to "brick wall", "cotton shirt" and the like.
The term 'open compound" is sometimes used for syntactic constructions like these, but it's a misnomer. We have to look at the grammar and lexical word formation. But I don't think you'd be tempted to call "brick wall" a compound, at least I hope you wouldn't!
An open compound is a combination of words so closely associated that they convey the idea of a single concept but are spelled as unconnected words.
The term "open compound" is a misnomer; in fact it's meaningless. "Open" implies separate, but "compound" implies inseparable.
Such expressions are separate words forming a syntactic construction, where the initial item is a modifier of the head. The other kind are morphological compounds composed of two (or occasionally more) smaller bases, e.g. "greenhouse", birdcage", "shortbread", "chewing-gum", "he-man" and so on.
Some are well-established, often lexicalised, while others are concocted on-the-hoof, e.g. "a custard-pie-in-your face sketch", but the distinction is still valid.