'A' is for the noun phrase, 'dark 12 months', not just the noun, 'months'. This noun phrase is singula. '12' is for the noun, 'months' only. It could be rephrased as '... after 12 dark months for Starbucks'. In this case, the noun phrase, 'dark months' is plural. There are 12.

Grammatically, "a dark 12 months" is short for "a dark period of 12 months" where "a period" is singular. This is not a rule that native speakers learn in school, it's just a pattern we get used to through experience without even thinking about it. Similar sentences include "A long 5 minutes" or "a quick 50 bucks" or "a miserable couple of days".

The others have answered. I'll just add a few more examples (from newspapers)>> "You kind of become obsessed for a good six months in the whole political sphere." npr.org "Charles Kennedy has had a bad few years." guardian.co.uk "I think CBQ will be a great leader, but I also expect him to make a few bad decisions and suffer through a few bad years." businessweek.com "That default is something Europe has been struggling to avoid for a good 18 months. " curiouscapitalist.blogs.time.com Apotheker had been on the job a disastrous 11 months, the board demanded his resignation, and then paid him more than $13 million in termination benefits. nytimes.com

‘A dark 12 months’ = ‘a bad year’ There are similar sentences using definite articles or no articles. His appointment comes after 12 bad months for Starbucks… (In this case you are just saying that the months were bad. The original adds the idea that Starbucks’ performance varies. This is just one possibility of many.) His appointment comes after the worst year for Starbucks… (there is only one worst year) His appointment comes after the 12 dark months…. (those that I already wrote about)

"Dark 12" is used the same way you would use the word "dozen": "After a dozen months" "He bought a dozen eggs"