Heat oven to 425 degrees F. Heat 1 tablespoon oil in a large skillet over medium-high heat. Season the chicken with 1/2 teaspoon each salt and pepper and cook skin-side down until the skin is golden brown, 6 to 7 minutes. Transfer to a large rimmed baking sheet skin-side up and scatter the orange wedges around the chicken. Roast until the chicken is cooked through, 8 to 10 minutes.
Meanwhile, discard all but 2 tablespoons fat from the skillet and return to low heat. Add the bread to the skillet and toss in the fat to coat, then sprinkle with 1/2 teaspoon each salt and pepper. Cook, tossing the bread occasionally, until crisp and lightly golden brown, 8 to 10 minutes. Remove from the pan.
Return the pan to medium-low heat, add the lemon juice to the pan and cook, scraping up all the brown bits, for 1 minute. Remove from heat, squeeze the roasted orange wedges into the pan, add the Dijon mustard and the remaining 1 tablespoon olive oil and whisk to combine.
Add the kale mix to the skillet along with the croutons and toss to coat. Serve with the chicken.