What is the odds of making a flush prior to any cards being dealt in Texas holdem?

The question essentially means the same as "What is the chance to get a flush if dealt 7 cards?" This is because from the view of one player in hold'em they will simply get 7 cards, 2 pocket cards plus 5 community.

If I trust my sampling program it says a flush occurs 3.02% of the time.

To calculate exactly you can calculate the permutations. What we're looking for are the number of permutations which create a flush. The first card can be anything, thus 52 options, then the next four cards must be of the same suit, so 12, 11, 10, and 9 options. The last two cards can again be anything, so 47 and 46 options. These is just one permutation, the ordering can be done (6c2) = 15 ways. Then divide these permutations by the total number of 7 card permutations to get our answer:

52*12*11*10*9*47*46 * (6c2) / (52*51*50*49*48*47*46) = 0.297

A tad bit off since we haven't excluded the straight flushes, which the sampling shows occur 0.03% of the time (the amount of our difference).