Preheat the oven to 425 degrees F. Spray a rimmed baking sheet or large casserole dish with cooking spray. Alternatively, you can line with parchment paper.
Grate the zest from the lemon into a large bowl, then cut the lemon in half. Set aside.
In the prepared baking dish, combine the potatoes, 1 tablespoon olive oil, 1 clove minced garlic, 1/2 teaspoon of the oregano, 1/2 teaspoon of the salt, and 1/4 teaspoon of the black pepper. Toss well to coat. Spread the potatoes out in a single layer. Squeeze one lemon half over the potatoes. Roast the potatoes for 15 minutes.
While the potatoes are roasting, pat the chicken dry with paper towels and season all over with the remaining 1/2 teaspoon of salt, and 1/2 teaspoon black pepper.
To the bowl with the lemon zest, mix 1 tablespoon olive oil, 2 garlic cloves, remaining 2 teaspoons of oregano, and red pepper flakes. Add the chicken and toss with your hands, making sure that you rub the seasoning under the skin as well.
After the potatoes have roasted for 15 minutes, toss the potatoes, then add the chicken to the pan, placing the pieces skin side up on top of the potatoes. Drizzle the chicken and potatoes with the remaining 1 tablespoon olive oil. Continue to roast until the chicken and potatoes are cooked through and everything is golden and crispy, about 30-40 minutes longer.
Transfer the chicken and potatoes to a platter or serving plates and sprinkle with the parsley.