Cut the chicken breast into bite-sized cubes and season evenly with sea salt and black pepper.
In a small bowl, whisk together the coconut aminos, rice vinegar, minced ginger, minced garlic, arrowroot powder, and red pepper flakes until smooth.
Heat the avocado oil in a large skillet or wok over medium-high heat.
Add the chicken to the skillet and sear, stirring occasionally, until golden brown and cooked through, approximately 6 to 8 minutes.
Remove the chicken from the pan and set aside; add the broccoli florets to the same pan with two tablespoons of water.
Cover the pan and steam the broccoli for 3 minutes until it is tender-crisp and bright green.
Return the chicken to the skillet and pour the sauce mixture over the ingredients.
Stir constantly for 1 to 2 minutes until the sauce thickens into a glossy glaze that coats the chicken and broccoli.
Remove from heat, drizzle with toasted sesame oil, and serve immediately over the warm brown rice.