So, you are right that "wein" is not really and adjective here, it is always a noun, but what you are wrong about (and what permanenthiatus is right about) is how it is being used. While "wein" is still a noun, it is also still -modifying- the noun "flasche". In English, you would say "I drank the whole bottle (of wine)", not "I drank the whole wine", thus, "bottle" is the head noun in what would be called a genitive construct. So most people probably wouldn't choose to translate "mit einer flasche wein" as "with a wine bottle", in all reality there are contexts where "wine bottle" and "bottle of wine" can actually mean the same thing.
I'm assuming you posted the guidelines because I called you a fool, I can apologize for that I suppose. But what I said about genitival constructions -is- true. Unless you can cite some source saying otherwise, I'm going to take the fact that I'm a few months from an MA in linguistics, and the fact that wikipedia's pages about linguistics topics are incredibly accurate, to back up my claim.
From wikipedia's entry on "Genitive Construction": "In grammar, a genitive construction or genitival construction is a type of grammatical construction used to express a relation between two nouns such as the possession of one by another (e.g. "John's jacket"), or some other type of connection (e.g. "John's father" or "the father of John"). A genitive construction involves two nouns, the head (or modified noun) and the dependent (or modifier noun). The dependent noun modifies the head by expressing some property of it. For example, in the construction "John's jacket", "jacket" is the head and "John's" is the modifier, expressing a property of the jacket (it is owned by John)."
So whether we are going with "wine bottle" as someone has said, or "bottle of wine" as you are saying, they are both considered "genitival constructs" grammatically, because in both cases a noun, "wine" is modifying another noun, "bottle". Here's where you probably think I'm confusing other users though: the fact that it is a "genitive construction" does not necessarily mean that it uses the "genitive case". Obviously in the sentence here there is a preposition present, "mit" requiring that the following determiner phrase (or noun phrase) be in the dative case, but that does not change the genitive nature of the determiner phrase.
This may be so technical as to not be of interest to any learner, and they can ignore it. But you seem to be accusing me of confusing other learners merely because you perceive me to be spreading misinformation, and I'm telling you that I am not.
Since I'm a linguist, perhaps I can help resolve some of the confusion over the expression Flasche Wein. I took a few minutes to research it in a German reference grammar.
The short answer (as the moderators have said) is that this is an "appositional" use of Wein. It is not genitive nor is it an adjective. You use it when you want to make a noun phrase modify another noun phrase, which is what makes it feel like an adjective or a genitive. A linguist would say that all three (apposition, adjective, and genitive) serve the same semantic function but with different syntax.
Linguists have a special set of grammatical terms that are intended to let us describe all the languages in the world and compare them to each other. (As one of the moderators said, we'd call this a "partitive.") Each language, however, has its own way of describing itself. When you're learning a language, you want to use the terms customarily used to describe that language--not the universal terms, which are usually more complex.
I see that there are lots of rules for when to use apposition, when to use the genitive, and when to make a compound word. I expect we'll learn those as we go along. For now, I think it suffices to know that when you want to say how much you have of something (e.g. a bottle of wine), you can use apposition to combine two nouns.
Hammer's German Grammar and Usage, 5th Edition (Durrell, 2013, section 2.7, "Genitive, Von, or Apposition?")
It depends on what kind of flask you're talking about. Those balloony wine flasks are called "Flaschen" as well (or "Ballonflaschen" if you want to be more specific). The flasks you use in chemistry are called "Kolben" and the little flasks you carry with you are "Fläschchen" (little bottles) or "Feldflaschen" (field bottles). If they are flat, they are sometimes called "Flachmann" (literally "flat man").
corrected it would be "mit einer Flasche des Weins" or "mit einer Flasche des Weines"
this genitive construction is not used here because it would require that the wine is a specific one which was mentioned before.
e.g.: You visit a friend who is a winegrower and has been raving about a certain wine for years. If you then get "eine Flasche dieses speziellen Weines" as a gift, you can show off "mit einer Flasche des Weins" at home.
oh and it is "mit einer Flasche" and not "mit eine Flasche". It is dative because of the "mit" here.
Dative follows this pattern: M, einem; F, einer; N, einem; P, einen. Genetive would follow this: M, eines; F, einer; N, eines; P, einer.
Feminine is the same for both Dative and Genitive, hence wataya's comment; here it is being used in the dative. Not a german scholar by any means, but I think it would be very awkward forming a genitive noun directly after a preposition like "mit".
Comments always appreciated :)