Cut the chicken breast into bite-sized pieces and toss in a small bowl with arrowroot powder, sea salt, and black pepper until evenly coated.
Heat the avocado oil in a large skillet or wok over medium-high heat until shimmering.
Add the chicken to the skillet and cook for 6-8 minutes, stirring occasionally, until golden brown and cooked through; remove chicken from the pan and set aside.
In the same skillet, add the toasted sesame oil, broccoli florets, and sliced red bell pepper, sautéing for 4-5 minutes until tender-crisp.
While the vegetables cook, whisk together the coconut aminos, rice vinegar, minced ginger, minced garlic, and red pepper flakes in a small bowl.
Return the cooked chicken to the skillet and pour the sauce over the chicken and vegetables.
Toss everything together for 1-2 minutes until the sauce thickens slightly and coats the ingredients in a glossy glaze.