What is the probability of flopping two pair?

2.02% for two pair that uses both hole cards, or 2.11% if you count the flops that become a full house.

Is the chance the same for AK and 72?

Yes. Any two different ranks have three matching cards each among the 50 unseen, so the count of flops is the same.

Probability of Flopping Two Pair

Both hole cards pair up on 2.11% of flops, 1 in 47.3. Most of those, 2.02%, are two pair; the rest are a full house.

What is the chance of flopping two pair?

To pair both hole cards, the flop must hold one of the three remaining cards of each rank. That is 414 of 19,600 flops, 2.11%, or 1 in 47.3. If the third flop card is a different rank, you have two pair: 3 x 3 x 44 = 396 flops. If it matches one of your ranks, you have a full house: 18 flops.

What an unpaired hand makes when both hole ranks hit the flop
Event	Chance	Odds	Flops out of 19,600
Both hole ranks on the flop	2.11%	1 in 47.3	414
Two pair (the third card is a new rank)	2.02%	1 in 49.5	396
A full house (the third card matches a hole rank)	0.09%	1 in 1,089	18

What about two pair with a pair on the board?

When one hole card pairs a card on the flop and the flop also pairs another rank, the hand is two pair too, but the pair on the board belongs to everyone. The first row above counts only flops that use both of your hole cards, which is the two pair that is yours alone.

Where do these numbers get used?

The chance to flop a hand is the first number in a plan. The pages below turn it into prices: what a call can cost, how many outs a draw has, and how many ways a hand can be dealt.

How were these numbers computed?

After two hole cards are dealt, 50 cards are unseen and the flop is any 3 of them, so there are C(50, 3) = 19,600 equally likely flops. For each starting hand we deal all 19,600, classify the five cards with our hand evaluator and count. Suits are symmetric, so one combination stands for every combination of the same hand. The closed forms on this page use binomial coefficients and give the same counts.

Source: GeorgeLiPoker's own exact count of the 52-card deck.

Questions

What is the probability of flopping two pair?: 2.02% for two pair that uses both hole cards, or 2.11% if you count the flops that become a full house.
What are the odds of flopping a full house with an unpaired hand?: 0.092%, or 1 in 1,089.
Is the chance the same for AK and 72?: Yes. Any two different ranks have three matching cards each among the 50 unseen, so the count of flops is the same.