Preheat oven to 400 degrees F.
Cut flatbreads into 8 wedges. Place wedges into a large bowl and drizzle with 4 tablespoons olive oil. Sprinkle with black pepper and toss to coat. Place on an ungreased baking sheet and lightly top with feta cheese. Bake for 5 to 8 minutes. Remove from oven and set aside.
Preheat grill to medium-high heat.
Brush eggplant with 4 tablespoons extra-virgin olive oil and season with salt and pepper.
Place on grill and cook for 2 minutes on each side or until tender. Remove from grill and dice. Add the eggplant to a bowl, stir in remaining ingredients, including 4 tablespoons of olive oil, and toss to combine. Serve with toasted pita chips.