The origin of "in like Flynn" is a bit unclear, but it's most likely a reference to Errol Flynn, a charismatic and successful Hollywood actor of the 1930s and 1940s. He was known for his handsome looks, swashbuckling roles, and his ability to charm his way out of any situation.
Therefore, "in like Flynn" came to signify someone who was always lucky and successful, and seemingly effortless in their achievements.
The mishearing "in like flint" is a humorous example of how language can evolve and change over time, often through informal use and misinterpretation.