I understand that it's possible to arrange these words this way, since "dobrou" is clearly linked to "Kávu" by case/number/gender, and word order is very flexible, but is it typical to separate the adjective and the noun this way? "Coffee they have good," is a bizarre sentence to me.
You usually add the information you want to stress at the end of the clause.
This sentence emphasises the fact that the their coffee is indeed good.
A more neutral way would be: Mají dobrou kávu.
This all depends on information already given in a conversation. If people are talking about a restaurant and complain about food, but then someone says "Kávu mají dobrou", it means he/she is pointing out that the coffee there is actually good. (it can also suggest that the coffee is the only thing good there)
"Jídlo je tam zlé, ale kávu mají dobrou." (The food is bad there, but they have good coffee.)
I am enjoying learning Czech on Duolingo, but some of the unnusual word order is slowing me down.
I understood the general meaning of "kávu mají dobrou" but I had to stop, scratch my head and read the comments. :) Would it be possible to add extra context to some of these sentences?
Duolingo does not work that way. Any context that makes sense is possible. Always.