Make the buffalo chicken filling: in a bowl, combine 1 cup cooked shredded chicken, 1/4 cup plain Greek yogurt, 1/3 cup buffalo sauce, 2 tablespoons chopped chives, 1 tablespoon dried parsley, and 1 teaspoon dried dill; stir until evenly coated.
Make the ranch-style yogurt sauce: in a separate bowl, combine 1 cup plain Greek yogurt, 1/2 cup finely chopped cilantro, 1 teaspoon garlic powder, 1 teaspoon onion powder, 1/4 cup chopped pickled jalapeños plus 2 tablespoons brine, juice of 1 lime, and 1 teaspoon kosher salt; mix until smooth.
Prepare tortillas and fillings: lay one tortilla flat and cut from the center to the edge to create four quadrants.
Assemble each wrap: spread the buffalo chicken in the bottom-left quadrant, place a handful of shredded romaine, chopped jalapeño/poblano, and chopped green onions in the top-left quadrant, spread the ranch sauce on the top-right quadrant, and add shredded cheddar and pepper jack cheese to the bottom-right quadrant.
Fold the wrap: fold the bottom-left quarter (chicken) over the lettuce, then fold that quarter over the ranch, and finally fold that quarter over the cheese so the wrap is fully folded into layers.
Cook until crispy: heat a drizzle of olive oil in a skillet over medium heat, add one assembled wrap, and cook 2–3 minutes per side until crisp and golden brown; repeat with remaining wraps.
Serve warm with extra buffalo sauce or ranch if desired.