In a small bowl, whisk together the coconut aminos, rice vinegar, honey, minced ginger, minced garlic, red pepper flakes, and arrowroot powder until the mixture is smooth and the starch is dissolved.
Heat the avocado oil in a large skillet or wok over medium-high heat until it begins to shimmer.
Add the cubed chicken breast to the hot pan and sear until golden brown and cooked through, approximately 6 to 8 minutes.
Remove the chicken from the skillet and set it aside on a plate, then add the toasted sesame oil to the same pan.
Add the broccoli florets and sliced red bell pepper to the skillet, sautéing for 4 to 5 minutes until they reach a tender-crisp texture.
Return the cooked chicken to the pan and pour the prepared sauce over the chicken and vegetable mixture.
Toss the ingredients constantly for 1 to 2 minutes until the sauce thickens into a glossy glaze that thoroughly coats the stir-fry.
Transfer the stir-fry to a bowl over the cooked brown rice and garnish with sesame seeds and sliced green onions before serving.