Cut the chicken breast into bite-sized pieces and season evenly with sea salt and black pepper.
In a small glass bowl, whisk together the coconut aminos, rice vinegar, sesame oil, and arrowroot powder until smooth.
Heat the avocado oil in a large stainless steel skillet or wok over medium-high heat until shimmering.
Add the chicken pieces to the hot skillet in a single layer and sear until golden brown and cooked through, about 6 minutes.
Remove the chicken from the skillet and set aside on a plate.
To the same skillet, add the broccoli florets, sliced red bell pepper, minced ginger, and garlic with two tablespoons of water.
Sauté the vegetables for 3 to 4 minutes, stirring frequently, until they are bright green and tender-crisp.
Return the chicken to the skillet and pour the prepared sauce over the mixture, tossing constantly until the sauce thickens into a glossy glaze.
Serve the stir-fry immediately over the warm cooked brown rice and garnish with red pepper flakes.