Most species of cockroaches do NOT fly.

According to 9th Edition of the Mallis Handbook of Pest Control, by Arnold Mallis, though most of the cockroach species do not fly, there are several that do including hundreds of tropical species. In the United States, it is more common for the male of particular species to fly including Supella longipalpa, Periplaneta, Blattella asahinai, Panchlora nivea, Arenivaga and Parcoblatta males.

Mallis, Arnold, and Dan Moreland. Handbook of Pest control: the Behavior, Life History, and Control of Household Pests. 9th ed. Cleveland, Ohio: GIE Media, 2004. Print.

Supella longipalpa ( Brownbanded cockroach): Males fly. Brownbanded cockroaches prefer dry, warm habitats. They can be found throughout the United States.

Periplanet (American Cockroach): The male specie will fly but they prefer to run when disturbed. The American cockroach prefers warm, humid, moist habitats and generally live outdoors. They can be found throughout the United States.

Blattella asahinai (Asian Cockroach): Males of the species fly. The Asian cockroach is prevalent in the Southeast in such states as Florida, South Carolina, Texas, Alabama, and Georgia. They prefer shaded mulched areas and can primarily be found out of doors.

Panchlora nivea (Cuban cockroach): The male of the species flies and is particularly attracted to light. Live primarily out of doors and can be found in Florida.