It can be done, but as mentioned, you'll have better success in the flats of the bays. In the surf you'll want to look for "sloughs" or areas where baitfish and other food can be corralled by fish looking to feed. Personally speaking, I caught a 12" or so flounder from the surf in the OBX a number or years back. You need a stripping basket and line that will get the fly down into the strike zone (intermediate, sinking, etc.). You can fly fish the surf in the OBX, but it's not a high numbers game. As mentioned, spin fishing is going to be your best bet. Hard to beat a two-hook downrig with some bloodworms, cut bait, or shrimp!
Attached you'll find some info that covers OBX fly fishing pretty well and is an amalgamation of information I collected from various sources, such as
OBX Fly Fishing , etc. There is now a dedicated fly shop in the OBX called
Outer Banks on the Fly and is located in Manteo, just west of Nags Head.
I'll be down there later this month for some R & R and will be tossing some feathers and fur into the surf. I'm not expecting much, but you never know!