Hi Malli
I don't know if flytraps get black spot disease or not (I haven't ever heard of that). But with black spot (which is a fungus) the black area is surrounded by yellow. Its not just a black spot. Leaves get a mottled yellowish color with black spots in the center and then the leaf dies and drops off. This is a common disease with roses and orchids and once infected, you can only control it, not eliminate it. It also spreads quickly (airborn) so its bad thing to have. That said, I doubt your VFT has black spot.
If you try a fungicide, you just follow the directions on the bottle for mixing it because it will depend on what brand you buy. There are quite a few out there. You might try 2 applications...once and then wait about a week and try it again.
Suzanne