Combine paprika, garlic powder, black pepper, onion powder, dried thyme, chili flakes, and salt in a small bowl. Mix well with your fingers to break up any clumps and ensure even distribution.

Pat the chicken leg quarters dry with paper towels. Rub olive oil all over the chicken, then generously coat each piece with the spice mixture, making sure to get some under the skin.

Cut potatoes into wedges and toss with a bit of olive oil and about 1 tbsp of the remaining spice mixture. Season evenly on all sides.

Preheat grill to medium-high heat. Place chicken on grill and cook for 25-30 minutes total, turning every 8-10 minutes. Add potatoes about halfway through cooking. Chicken is done at 165 degrees Fahrenheit internal temperature with caramelized skin. Potatoes should be golden and crispy.

Toss coleslaw mix with mayonnaise and lemon juice until evenly coated. Mix gently to avoid over-working the vegetables.

Arrange grilled chicken in the center of a plate, surround with crispy potato wedges, add a portion of coleslaw to one side, and fan out cucumber slices. Sprinkle chili powder on top for garnish. Serve immediately while hot.