Interstate Movement of Feeder Flies within the Continental US
Fruit flies (D. hydei, D. melanogaster, and D. willistoni), house flies (Musca domestica), blue bottle flies (Calliphora vomitoria), and black soldier flies (Hermetia illucens) do not require any USDA permits for interstate movement.
Other Movements, Including Other Species of Flies
Importation of the feeders listed above often requires a VS permit, and certain species above may require USDA permits for importation. Most other species are likely regulated for all types of movement, including intrastate, interstate, and importation. All imports would also require a FWS permit if you are the one importing (the personal pet exclusions I know of have too small of a limit on number of specimens to be applied here).