Combine the olive oil, balsamic vinegar, honey, lemon juice, Dijon mustard, dried oregano, dried basil, garlic powder, onion powder, salt, black pepper, and red pepper flakes in a mixing bowl or large freezer bag and whisk until smooth.
Add the pounded chicken breasts to the marinade and turn to coat completely; seal the bag or cover the bowl.
Marinate at room temperature for 30 minutes or refrigerate up to 12 hours for more flavor; if refrigerated, remove the chicken 15–30 minutes before cooking to come toward room temperature.
To grill: preheat the grill to about 400°F, clean and oil the grates, then grill the chicken undisturbed 5–7 minutes per side until an instant-read thermometer registers 165°F; let rest 5 minutes before slicing.
To skillet-cook: heat 1 tablespoon olive oil in a large nonstick or cast-iron skillet over medium-high heat; when very hot, add chicken and cook undisturbed 3–4 minutes until deeply golden, flip, cover, reduce heat to medium, and cook about 5–7 more minutes until internal temperature reaches 165°F.
To bake: preheat the oven to 425°F and lightly grease a baking dish, drain the chicken from the marinade, place in the dish, and bake uncovered 16–18 minutes for ~1/2-inch thick chicken (increase time for thicker pieces) until internal temperature reaches 165°F; let rest before serving.