Preheat your grill to medium-high heat (around 400°F). Mix olive oil, smoked paprika, and minced garlic in a small bowl. You'll want this brush-ready because we're moving fast once heat hits.
Season your sliced chicken with sea salt and half the paprika mixture. Sear the chicken on the grill for 3-4 minutes per side until it's got golden color and no pink inside. Let it rest on a plate for a minute while you move to the flatbreads.
Brush both sides of each flatbread with the remaining garlic-oil mixture. Place them directly on the grill grates and watch them closely—don't walk away for more than 2 minutes or you'll get char spots (mine always does and honestly it's fine, but watch it).
Flip the flatbreads after 2-3 minutes when you see those pretty grill marks appear. Cook the other side for another 2 minutes until it's just barely firm but still pliable. Transfer to a clean cutting board immediately.
Grill your sliced bell peppers and red onions for 2-3 minutes, stirring once so they get slightly charred at the edges. They should still have a little crunch, not be totally soft. Set them aside on a separate plate.
Slice your grilled chicken into bite-size pieces if they're not already. Toss it with lemon juice and fresh cilantro—this combo right here is what makes the grilled flatbread party appetizer taste so fresh instead of heavy.
Top each warm flatbread with chicken, grilled vegetables, cherry tomatoes, and crumbled feta. Drizzle any extra lemon juice over top and serve immediately while the flatbreads still have that warmth. People eat these way faster than you'd expect.