1. mod. successful, in a variety of contexts, sex being the major one. (The in can be construed to be the in of in coitu. Not to be confused with the James Coburn movie, In Like Flint. This Flynn is associated with Errol Flynn, the late film actor, but appears to have occurred earlier.) A few nice words, a bit of bubble, and you’re in like Flynn.
2. mod. an elaboration of in, in any of its senses. You got the role! You’re in! You’re in like Flynn!