In a large bowl, whisk together olive oil, lemon juice, garlic, smoked paprika, pepper, and oregano. Add chicken and toss to coat. Cover and marinate in the refrigerator at least 30 minutes, up to 2 hours.
In a separate bowl, toss bell peppers, onion, and zucchini with Dale's Seasoning. Marinate in the refrigerator 30 minutes to 1 hour, stirring occasionally.
If using wooden skewers, soak in water at least 30 minutes before threading.
Preheat oven to 425 degrees F.
Thread marinated chicken and vegetables onto skewers, alternating pieces. Place on a wire rack set over a baking sheet, or directly on a foil-lined sheet pan sprayed with cooking spray.
Bake 20 to 25 minutes, flipping halfway through, until chicken is cooked through.
For a slightly charred finish, broil on high 2 to 3 minutes at the end.