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If you get a Togetic in Pokemon Emerald it can learn Mimic from the move tutor in Fortree City, then you can get a Togekiss with Mimic and Serene Grace by trading it to Gen 4 and evolving it. Then, in a double battle a faster Pokemon (like Prankster Whimsicott) can use Beat Up (it is not a status move but Prankster is helpful later) and Togekiss mimics it. The next turn you can use Tailwind to make Togekiss faster than most Pokemon and have it use the 6-hit Beat-Up (unless Whimsicott faints or has a status condition) with each hit having a 20% flinch chance thanks to King's Rock 10% doubled by Serene Grace. How often will the opponent flinch in this case?

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A 20% flinch chance per hit happening 6 times has a 73.7856% chance of occurring (the math being (1-(8/10)^6)*100).

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Generation V onward
Serene Grace boosts the 10% flinch chance due to King's Rock or Razor Fang to 20%.
Source: Bulbapedia
The question never said the Togekiss would transfer to anything newer than gen 4.
@megaMHX you're right, my bad.
It did mention Prankster Whimsicott as the teammate, where both Whimsicott and the Prankster ability itself wouldn't exist until 5.