Hmmmm..... I'm thinking Isonychia- it's called by a lot of different names like White Gloved Howdy, Leadwing Coachman, Slatewing Dun, etc but probably the most common one is "Mahogany Dun". 2 tails, mahogany brown body and slate gray wings, about a size 12 but can range from a 10-14-- and the timing seems right.
It's a very common hatch throughout the East on freestone streams and a bit unusual-
It often hatches in 2 groups-- one in early season May-June that often runs larger size 10-12 and then another in late summer into Sept-October often a bit smaller size 12-14.
The nymphs are good swimmers and typically swim to rocks on the stream (like stonefly nymphs) and emerge there rather than in the water like most mayflies- look for their cases on the tops of rocks midstream. In many streams the nymphs will have a white stripe down their back. Good nymph imitations are slender with dark brown dubbed bodies, but generic ones like Prince Nymphs and Zug Bugs often work well. You can strip them like a streamer, just a bit slower. Because the nymphs typically swim and emerge on rocks emerger patterns and duns are not as available to the fish as the spinners. Wets like the Leadwing Coachman can still be effective though to imitate emergers or drowned adults, and dry fly patterns with CDC, or Comparaduns can work well too for the duns, though they're often not as available as other mayfly duns that have to sit on the water while their wings dry off. (once the they emerge on a rock into the dun, they can simple fly off.) Some duns do get blown into the water, and there are some streams where actual emergence in the water seems to be more common. And even if there aren't any natural duns on the water, trout seem to go out of their way to whack imitations. They must taste good-- maybe like chocolate?
My favorite dry pattern for this hatch is a Dun Variant- dun tail, brown quill body and an oversize medium dun hackle collar (no wing). You can skitter this across the surface or dead drift it and it's a great imitation for the spinner. I usually tie them on a size 14 hook with size 12 hackle.
The critter in your pic looks like an Iso spinner with gray wings-- the dun has dark veins in it's gray wings which are pretty prominent.
Here some more detailed info and pics from troutnut (a great site for this kind of stuff).
Does this seem like it could be a match?