Preheat the oven to 350 degrees F (175 degrees C).
Combine flour, garlic powder, onion powder, paprika, salt, and black pepper in a shallow bowl. Reserve 1 tablespoon of mixture for later use.
Dip sliced chicken into the flour mixture to coat both sides. Place on a plate.
Heat 3 tablespoons olive oil and butter in a skillet over medium-high heat. Add eggplant and onion and cook until soft and browned, 5 to 10 minutes. Season with salt and pepper; transfer to a baking dish. Cook zucchini and bell pepper in the same skillet over medium-high heat until softened, about 5 minutes. Season with salt and pepper and transfer to the baking dish with the eggplant.
Add additional oil to the skillet if needed and brown chicken on both sides, about 5 minutes. Transfer chicken to the baking dish with the vegetables. Pour tomatoes into the same skillet and add reserved flour mixture and dill paste. Bring to a boil, remove from heat, and pour into the baking dish. Top with feta cheese.
Bake in the preheated oven until bubbly, 30 to 40 minutes. Sprinkle with fresh dill.