Warm the olive oil in a large, non-stick skillet over medium heat.
Add the ground chicken and cook until no pink remains.
Move the chicken to the side of the skillet, and add the chopped onion, bell peppers, and carrots. Sauté until soft and fragrant, about 5 minutes.
Stir the minced garlic, onion flakes, paprika, yellow mustard powder, salt, and pepper into the chicken and veggies. Mix until well combined.
Add the ketchup, tomato sauce, Worcestershire sauce, and apple cider vinegar to the skillet and stir well.
Reduce the heat to low, cover the skillet, and let the mixture simmer for about 5 minutes.
Serve ground chicken sloppy joes over toasted brioche buns, and enjoy!