Preheat a waffle iron to high. Combine the brown sugar, paprika, coriander, mustard powder, onion powder, garlic powder, cayenne, 1 1/2 teaspoons salt and 1/4 teaspoon black pepper in a small bowl. Reserve 1/2 teaspoon of the spice mixture for the syrup.
Halve each chicken breast crosswise. Lightly pound the thicker pieces between 2 pieces of plastic wrap with the flat side of a meat mallet or heavy skillet so that they are the same thickness as the other pieces. Toss the chicken with the vegetable oil, then rub all over with the spice mixture.
Generously brush the waffle iron with vegetable oil. Put a larger chicken piece in the center of each back quadrant of the waffle iron and a smaller piece in each of the front quadrants. Press the lid down to flatten the chicken and cook, pressing on the lid periodically, until the chicken is just cooked through, 3 to 5 minutes. Transfer to a platter and repeat with the remaining chicken.
Meanwhile, combine the maple syrup, vinegar and the reserved 1/2 teaspoon spice mixture in a small saucepan over high heat. Cook until bubbling and thick, about 5 minutes. Drizzle over the chicken.