The story
First attested in 1942 (see quotations below). The slang sense is from the canine vulva resembling the cleft shape of the snack.
Etymology from Wiktionary, CC BY-SA 4.0.
fortune cookie
Today it means: A type of hollow snack, common in westernized Chinese cuisine: a crisp sugary wafer containing a message on a narrow strip of paper, generally with a wise or vaguely prophetic message or random numbers usable in a lottery printed on the paper. Full definition →