In a small bowl, whisk together tamari, rice vinegar, honey, sesame oil, ginger, garlic, red pepper flakes, arrowroot powder, and water to create the sauce.
Heat avocado oil in a large skillet or wok over medium-high heat.
Add the diced chicken breast to the skillet and cook until golden brown and cooked through, about 5-7 minutes.
Remove the chicken from the skillet and set aside.
Add the broccoli florets and sliced red bell pepper to the same skillet, adding a splash of water if needed to steam-cook until tender-crisp.
Return the chicken to the skillet and pour the prepared sauce over the mixture.
Stir constantly for 1-2 minutes until the sauce thickens and coats the chicken and vegetables evenly.
Serve the stir-fry immediately over the warm cooked brown rice.