*note* The Venus Flytrap's origin is not definite and many attributes are unknown. The plants below are found to be some of the closest related species to the Venus flytrap based on what scientists do know.

The king Sundew (above right)

Drosera regia, commonly known as the king sundew, is a carnivorous plant in the sundew genus drosera. The Drosera Regia has many unusual relict characteristics, and these along with molecular data from phylogenetic analysis contribute to the evidence that it possesses some of the most ancient  characteristics within a genus. Some of these characteristics are also seen in the Venus flytrap, and this suggests a evolutionary relationship. 

The Waterwheel plant (above left)

Aldrovanda vesiculosa, commonly know as the waterwheel plant, is also known as a snap-trap; just like the Venus flytrap. The difference is the Venus flytrap closes around an insect in just 0.3s or faster, while the waterwheel use thin translucent traps to snare copepods and other aquatic invertebrates. Also, while both share the unusual carnivorous trait, the Flytrap is a land plant, while the waterwheel is an aquatic plant.