Since the term reflexive already refers to what is directed or turned back on itself, smushing it together with the word self doesn't accomplish anything, perhaps besides signaling the intent to move forward. But so does a rear end collision at a red light. And what is happening when an artist refers to a century-old stereotype or a half-century old taboo is hardly reflexive; it demands foreknowledge of the stereotype and associated taboos, and perhaps even some inkling that these taboos have become a little bit rediculous.
(Reflexive, to my mind, would refer to something like Hamlet putting on a play about brother-murder in a play called Hamlet.)
And does it really make sense to call it irony when what's depicted is supposed to be just an exaggerated version of the truth? I would call it a humorous hyperbole mocking two different targets and call it a day.