Question: In English, we say "degree of darkness." In a document, I stumbled on the phrase
"cantidad de oscuridad," which means the "amount of darkness." This becomes really awkward in English. Is this phrase correct or common in Spanish?

Answer: 
This is a case where English and Spanish coincide and the expresions can be translated word-by-word. Your English example would be "grado de oscuridad" and it is perfectly understandable, if not common. The string of words you are asking about (I hesitate to call it a Spanish expression) sounds awful. So **yes**, you are right to be suspicious.

Of course the whole point is that you do not measure darkness. You can talk about the quality of the darkness, and that is why "degree" works in both languages.
In Spanish, the expression `cantidad de luz` is used to mean [illuminance](https://en.wikipedia.org/wiki/Illuminance). I can understand `cantidad de oscuridad` as the inverse: the less *amount of light* (= the less illuminance), the more *amount of darkness*.

The expression doesn't sound bad (this time I disagree with Rodrigo). It sounds natural, given common phrases as `más/menos oscuridad`, `mucha oscuridad`, `cuánta/tanta oscuridad`.

But I don't work in architecture or any field where that expression could be used, so I can't definitely assert whether it is commonly used or not.