Which word fits best in this context: No such _____ He flatly refused?

The word "luck" fits best in the given context because it conveys the idea of someone feeling that there is no favorable circumstance or good fortune regarding a particular situation. The phrase "No such luck" is an idiomatic expression commonly used to indicate that a desired outcome is not possible or has not occurred, suggesting disappointment or frustration about the situation.

The other choices, while related to possibilities or outcomes, do not capture the same idiomatic sense. "Decision," "chance," and "opportunity" do not express the notion of fortune or randomness in the way that "luck" does. Therefore, in this sentence, "luck" most accurately reflects the speaker’s intent to communicate a flat refusal in a context where one might hope for a positive turn of events.