In a food processor, pulse the cooked chickpeas, onion, garlic, herbs, cumin, paprika, baking soda, flour, salt, and pepper until combined but still slightly chunky. Refrigerate for 15 minutes to set.
Form small round patties (about 1.5 inches wide). Heat the olive oil in a pan over medium heat and cook the falafel for 3-4 minutes per side until crispy and golden brown. Drain on a paper towel placed on a plate.
Mix Greek yogurt, grated cucumber, garlic, lemon juice, olive oil, and herbs to make the tzatziki sauce. Season with salt and pepper.
Warm the flatbreads slightly.
Spread a generous layer of tzatziki.
Add the falafel, shredded lettuce or greens, cherry tomatoes, pickled onions, radishes, and crumbled feta.
Garnish with fresh herbs and an extra drizzle of tzatziki.
Wrap or fold depending on the type of bread you are using, and serve immediately.