Search for Dionaea (genus) muscipula (species) here:
http://www.cites.org/eng/resources/species.html
You'll see this entry
CITES Appendix II
All parts and derivatives, except:
a) seeds, spores and pollen (including pollinia);
b) seedling or tissue cultures obtained in vitro, in solid or liquid media, transported in sterile containers;
c) cut flowers of artificially propagated plants; and
d) fruits and parts and derivatives thereof of artificially propagated plants of the genus Vanilla.
CITES Appendix II
Designates all parts and derivatives, except:
a) seeds, spores and pollen (including pollinia); and
b) tissue cultures and flasked seedling cultures.
Here is a link to what an Appendix II listing means:
http://www.cites.org/eng/app/index.shtml
Appendix II lists species that are not necessarily now threatened with extinction but that may become so unless trade is closely controlled. It also includes so-called "look-alike species", i.e. species of which the specimens in trade look like those of species listed for conservation reasons (see Article II, paragraph 2 of the Convention). International trade in specimens of Appendix-II species may be authorized by the granting of an export permit or re-export certificate. No import permit is necessary for these species under CITES (although a permit is needed in some countries that have taken stricter measures than CITES requires). Permits or certificates should only be granted if the relevant authorities are satisfied that certain conditions are met, above all that trade will not be detrimental to the survival of the species in the wild. (See Article IV of the Convention)
So no, you don't need a CITES permit for Venus fly traps. However, you will need a phytosanitary permit for them unless they are in sterile cultures (tissue cultures, aka
in vitro). You'll also need an import permit if you plan on importing more than a few plants. I've spoken with Carolyn Fitzgerald at the USDA office and I remember the magic number of plants to be 12. If you're importing more than 12 plants, you need an import permit.