Vinaigrette: In a bowl or glass jar, combine olive oil, basil, oregano, both vinegars, garlic, honey, chili flakes, salt, and pepper; mix well.
Chicken Prep: In another bowl, mix the chicken, half of the vinaigrette, and smoked paprika. Thread the marinated chicken onto skewers.
Grill Peppers: Grill the peppers on medium-high until charred. Cover in a bowl and let steam for 10 minutes, then peel, deseed, and slice. Submerge in the remaining vinaigrette.
Grill Chicken: Grill skewers until charred and cooked through, about 10-12 minutes, turning occasionally.
Sauce: Mix Tzatziki sauce, mayo, and lemon juice. Add feta cheese and mix well.
Assemble: Layer rice in a bowl, top with grilled peppers and chicken skewers. Add dollops of feta and drizzle with Tzatziki sauce.