Remove the steak from the fridge and allow it to come to room temperature (20 to 30 minutes).
Meanwhile, combine the smoked paprika, cumin, oregano, salt, pepper, and garlic powder in a small bowl. Briefly set aside.
In a medium bowl, combine the cucumber, tomatoes, and red onion. Drizzle with red wine vinegar and olive oil and toss to combine. Season with a tiny pinch of salt and pepper if desired. Cover and refrigerate until ready to use.
Pre-heat a grill or grill pan over high-heat.
Rub the steak all over with the spice mixture. Once seasoned, slice the steak crosswise into two pieces of roughly equal size. (If you’re using a grill pan, you may want to cut the steak into 3 pieces so that they’re not too long for the pan.)
Place the steak on the hot grill and cook for about 2½ to 5 minutes per side for medium rare. (Skirt steak varies so much in thickness, which is why the cooking window is so large here. In general, it cooks quickly so be careful not to overdo it, especially if you have a thin steak! The piece of steak with the narrow “tail” tends to cook more quickly, so you’ll want to take that off the grill before the other piece(s).) Transfer the steak to a cutting board and allow to rest for 5 minutes. Slice thinly against the grain.
While the meat rests, warm the flatbreads. Place them on the hot grill for about 1 minute per side, just until grill marks appear.
Spread each flatbread with ¼ cup of hummus. Top with sliced steak and the cucumber mix. Garnish with feta, parsley, and crushed red pepper if you like.