To prepare piadini, lightly spoon flours into dry measuring cups; level with a knife. Combine flours, 1 teaspoon salt, baking powder, thyme, and rosemary in a large bowl. Add 3 tablespoons oil; stir with a whisk until evenly distributed. Add water; stir until dough forms. Turn dough out onto a lightly floured surface; knead 2 minutes. Place in a bowl coated with cooking spray. Cover with plastic wrap; let rest at room temperature 30 minutes.
To prepare greens, heat 1 1/2 teaspoons oil in a large nonstick skillet over medium heat. Add garlic; cook 2 minutes or until lightly browned, stirring constantly. Add chard; cook 8 minutes or until tender, stirring frequently. Add spinach; cook 3 minutes or just until wilted, stirring frequently. Stir in juice, pepper, and 1/8 teaspoon salt. Remove from heat; keep warm.
Divide dough into 24 equal portions; shape each portion into a ball. Working with one portion at a time (cover remaining dough to prevent drying), roll into a 4-inch circle. Repeat procedure with remaining dough. Stack dough circles between single layers of wax paper to prevent sticking. Heat a large nonstick or cast-iron skillet coated with cooking spray over medium-high heat. Add 2 dough circles; cook 1 minute on each side or until golden brown. Cover and keep warm. Repeat procedure with remaining dough circles. Spoon about 2 tablespoons greens onto each flatbread; fold in half. Serve immediately.