[pzhon]

13 flops are trips. 13
There are 13*12 ways to choose the ranks of paired flops, and these are either 2-tone or rainbow. 312
There are 13C3 ways to choose the ranks of unpaired flops. These can be monotone, two-tone in 3 ways, or rainbow. 1430
Total: 1755

This assumes you haven't seen your hand.

There are abstract tools (Polya counting) that work for this type of problem, but they are more complicated than a direct calculation.