Combine paprika, smoked paprika, garlic powder, onion powder, oregano, salt, and black pepper in a small bowl. Mix well until evenly distributed.

Pat chicken leg quarters dry with paper towels. Rub them generously with olive oil on all sides. Apply the spice rub liberally to both sides of each leg quarter, pressing the seasoning into the skin. Let sit at room temperature for 15 minutes.

Cut potatoes into thick wedges, leaving the skin on. Toss with salt and pepper. Set aside.

Combine coleslaw mix and diced cucumber in a medium bowl. Whisk together mayonnaise and lemon juice in a separate bowl, then pour over vegetables and toss well. Season with salt and pepper to taste. Let sit for 30 minutes before serving.

Heat grill to medium-high heat and oil the grates. Place potato wedges on the grill cut-side down and cook for about 15 minutes, flipping halfway through, until golden and crispy. Add seasoned chicken leg quarters skin-side down after a few minutes and cook for 15 to 20 minutes total, flipping halfway through, until the skin is deeply caramelized and internal temperature reaches 165°F.

Arrange grilled chicken, crispy potato wedges, fresh cucumber slices, and creamy coleslaw on plates. Sprinkle with chili flakes for garnish and serve immediately.