Question

Does venus flytrap does photosyntises

Answer 1

Yes, The venus flytrap does photosynthesis.  Photosynthesis is actually the primary source of energy for Venus flytraps. 

Answer 2

Yes.
Venus flytrap does perform photosynthesis in order to synthesize its own food.
It possess green and chloroplast containing structures and hence, takes part in photosynthesis.
In fact, photosynthesis is its major source of food.