Cut the skirt steak into 3-inch wide sections – this makes it easier to grill and cut later. Season on all sides with kosher salt and set aside.
Make the sauce for the steak by juicing the citrus – aim for about a cup of juice. Add the juice to a large mixing bowl and add the rice wine vinegar, soy sauce, Sriracha, ginger, and garlic. Add about half of the citrus bodies to the bowl.
Heat the grill for high heat, two zone cooking. Coat the skirt steak and remaining citrus halves in a little oil. Grill the steak and citrus halves for 2 to 4 minutes per side. Move the finished steaks to the sauce and squeeze in the grill citrus bodies. Let the steak rest in the sauce for 5 to 30 minutes.
Slice the steak against the grain and serve over your favorite cooked rice with extra Sriracha and sesame seeds to finish.