flares and mud flaps both serve a different purpose. the flares keep you from throwing debris up and out to the sides, mudflaps keep you from throwing debris rearward. I'm not just talking mud and stuff stuck in the tires, small rocks and things on the road get tossed up too. I think the DOT wants flaps on there if the centerline of the tire is below the lowest part of the rear of the wheel well, and flares have to cover any part of the tire that extends outside the wheel well.
Your local laws may differ though so as stated above it's best to check. your state's DMV website should have that info available for you.