A fink, whether in prison or not, is a derogatory reference to someone who seeks favor from the authorities for information that they have learned in confidence.
It’s said that a fink is someone who sings to the police or the boss like a canary, which all becomes logical when you realize that fink is the Yiddish word for “finch.”
Finches, or finks, are a family of songbirds, of which the canary is one of the most vocal.