Position a rack in the upper third of the oven and preheat to 450 degrees F. Coat a rimmed baking sheet with cooking spray. Toss the chicken pieces with the sour cream, garlic powder, cayenne, half the lemon zest, 1/4 teaspoon salt and a few grinds of black pepper in a large bowl to coat. Set aside.
Put the cornflakes in a shallow dish and stir in the olive oil, 1 tablespoon thyme and a pinch each of salt and black pepper. Coat the chicken in the cornflake mixture, pressing to adhere. Place on the prepared pan and lightly coat with more cooking spray. Bake until lightly browned on top, about 15 minutes.
Meanwhile, mix the butter with the remaining lemon zest and 1 tablespoon thyme in a medium bowl. Season with salt and black pepper and set aside.
Remove the baking sheet from the oven and move the chicken to one side. Arrange the waffles in two rows on the other side of the pan, overlapping them. Bake, flipping and rotating the waffles halfway through, until a thermometer inserted into the thickest part of the chicken registers 165 degrees F and the waffles are toasted and hot, 10 to 15 minutes.
Spread the lemon-thyme butter evenly over the waffles. Serve the chicken and waffles with maple syrup.