The clue is: “Go fly a kite!”
The answer is SITONIT Doesn’t that mean, “Stick it up your ass!”?
Your answer was a catchphrase on the 70’s TV show Happy Days, so how offensive could it possibly be? I submit “go jump in the lake” (i.e. go drown yourself) is much worse.
The two phrases have identical meanings: “Leave me alone, you jerk.” You’re finding nuance where none is intended.