a royal flush is not the only "unbreakable nuts".
sometimes, a straight flush is unbreakable.
example: if the flop is 5d, 7d, 8d and i am holding the 6d and 9d, my hand is unbeatable regardless of what other cards come out and what other players hold.
it is important to remember there is no difference than a straight flush and a royal flush except that the royal flush is the highest straight flush there is.
also, the only hands that are unbreakable at the flop are straight flushes, and you must be holding the highest card of the straight flush in your hand.
there is no way to eliminate the possibility of an eventual straight flush. no matter what 3 cards fall, 2 additional cards and 2 cards in an opponent's hand could make a straight flush... making even a flopped 4 of a kind in Aces beatable.
therefore, i believe to find the odds of an unbeatable hand on the flop to simply take the odds of flopping a royal flush, and multiply that by 2/5 (the odds of holding the top card of the flopped straight flush). i could be wrong, but i believe that would give you the answer you are looking for.
1/650000
;) No, a 2-pair can be cracked by a higher 2-pair or set that comes to Turn or River, assuming the board is dry that doesn't allows any flush/straight possibilities. – user1165 Jan 27 '15 at 6:50