WARNING: This contains maths!!
The odds of flopping quads with a PP are about 407 to 1 or 1/408, which we'll call 'p'. The odds of flopping it twice in a single SnG obviously depends on the number of hands that take place, which we'll call 'n'.
If you're after the odds for exactly twice the formula is:
(p^2) *[ (1-p)^n-2 ] * n! / [ 2! * (n-2)! ]
Although this assumes that you have a PP every hand. The probability of being dealt a pocket pair is 16 to 1 or 1/17 and the chance of flopping quads with a non-PP hand is 9799 to 1 or 1/9800. So the overall chance of flopping quads in any one hand is:
(1/17) * (1/408) + (16/17) * (1/9800) = 1/4613 roughly, which we'll redefine as 'p'.
So using the previous formula, assuming a nice round number of hands in the SnG, say 100. The odds of flopping quads exactly twice in a SnG would be approximately 1 in 3584.
If you wanted to know the probability for flopping quads twice or more in a sample you would have to subtract the probability of it happening exactly once and not at all from 1, adjusting the formula in the appropriate manner. I.e.
1 - (p^1) *[ (1-p)^n-1 ] * n! / [ 1! * (n-1)! ] - (p^0) *[ (1-p)^n ] * n! / [ 0! * (n)! ]