Use the same tree-diagram process that I described previously in your higi-low stud problem:

Start with a hand of three diamonds. There are 49 cards left. How many more diamonds are left? How many more "non-diamonds?" Draw the branches and determine the probabilities.

Then do the next card, branching again from the original two branches. There will be 48 cards left - based on the first set of branches, how many diamonds would be left and how many "non-diamonds?" - use this info to determine the conditional probabilities.

...and so on and so on until you get branches with at least 2 more diamonds - terminate these branches. Also terminate branches where you get enough "non-diamonds" to make a flush impossible.