Holding two unsuited cards and flopping a four flush.

You are looking for any of the 24 cards that are the same suit as either of the two cards that you hold. Then you are looking for any of the 11 cards that are the same suit as the first flop card. Then you are looking for any of the 10 cards that are the same suit as the first two flop cards. Then divide by the number of combinations. That gives you:

(24 * 11 * 10) / (50 * 49 * 48) = 2.245%

Holding two suited cards and flopping a flush.

You are looking for any of the 11 cards that are the same suit as the two cards that you hold. Then you are looking for any of the 10 cards that are the same suit as the first flop card. Then you are looking for any of the 9 cards that are the same suit as the first two flop cards. Then divide by the number of combinations. That gives you:

(11 * 10 * 9) / (50 * 49 * 48) = 0.842%

Holding two suited cards and flopping a four flush.

You are looking for any of the 11 cards that are the same suit as the two cards that you hold. Then you are looking for any of the 10 cards that are the same suit as the first flop card. Then you are looking for any card that DOES NOT match the suit of the first two cards, there are 39. Then divide by the number of combinations. That gives you:

(11 * 10 * 39) / (50 * 49 * 48) = 3.648%

That is the chance of flopping the four flush on the first two cards of the flop. There are two other ways to flop a four flush that have an equal chance: (1) matching the suit of the first and third cards, (2) matching the suit of the second and third cards.

So, you have 3 * 3.648% = 10.944%