"The flight crew".
This is a noun phrase with "crew" as head and the noun "flight" as attributive modifier.
There is no adjective present.
Steady on there, Paul.
I like your explanation, but that doesn't stop it being an open compound noun.
"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."
I think the rigidity of your definitions is undoing you a little.