So this question asks about forming adjectives from nouns, but no clear answer is really given for a general method. In english, you can just use a noun as a adjective without any modification by placing the modifing noun before the modified noun. For instance, "chicken soup" chicken in this case is a noun adjunct. Does this work in latin? Can I say "pullum jus" for "chicken soup"? If I do this with two words of different genders (I fail to think of an example, but I'm sure it's possible) do I have to change the adjunct's gender to match?
Latin doesn't really form noun phrases in the same way that English does, by stringing together a collection of modifying nouns before the original noun. To a Roman, the phrase pullus iūs would have probably been interpreted as something akin to chicken and soup.
The only time you'll really find two nouns of the same case (and often number as well as gender) next to each other is if they are in apposition to each other, like in the following example, where is māgnus imperātor is in apposition to Gāius Iūlius Caesar.
Tōtum Galliae vīcit Gāius Iūlius Caesar, is māgnus imperātor ac reī pūblicae Rōmānae sub iugō attulit eius populum.
Gaius Julius Caesar, that great general, conquered the whole of Gaul and brought her people under the yoke of the Roman Republic.
If you want to construct a noun phrase like chicken soup (or others), the genitive of description is usually used. The ablative of description can also be used, but, to the best of my knowledge, it is not quite as common (examples might include phrases like vir summā virtūte). Using either of these, the phrase chicken soup can be rendered as such:
That said, however, be cautious when using the genitive or ablative to describe a noun; there is often a suitable adjective or alternative noun. Be cautious, most especially when you are working with abstract concepts. See this excellent answer by kkm for a good explanation of this.
The typical choice in Latin is to derive an adjective from the noun. I would translate "chicken soup" as ius gallinaceum. Deriving adjectives is nontrivial but inevitable. A genitive is a good second option, but not the primary choice in my experience. A noun can't be used as an adjective as you would in English, so you always need something more elaborate than chaining nouns.