►Toss shrimp with lemon zest, garlic, and 1 tablespoon olive oil in a medium bowl. Season with salt. Thread shrimp on wet wooden skewers (about 4 per skewer), transfer to a platter or other large dish, and set aside.
►Heat grill to medium-high. Grill shrimp until opaque and slightly charred around the edges, about 6 minutes total. Remove from grill and set aside. When shrimp are cool enough to handle, remove tails and discard.
►Reduce grill heat to medium-low. Turn dough out onto a floured surface and divide into 4 pieces. Roll each piece into a 7-inch-long oval and brush both sides with olive oil. Place flatbreads directly on grill grates and cover grill. Cook, checking every 2 minutes, until dough bubbles and stiffens and flatbreads have visible grill marks on the bottom, about 4 minutes. Flip flatbreads, cover grill, and cook 1 minute. Remove from grill.
►Divide pesto among flatbreads and spread to coat the surface. Add 4 to 5 shrimp to each flatbread and top with crumbled feta. Return flatbreads to grill, cover, and cook, checking every 2 minutes, until cheese is softened and dough is fully cooked, 3 to 4 minutes. Remove from grill.
►Sprinkle flatbreads with chopped olives, chives, and black pepper.