Pat the chicken breast chunks dry with a paper towel and toss them in a bowl with arrowroot powder, sea salt, and black pepper until evenly coated.
In a small glass jar, whisk together the coconut aminos, rice vinegar, honey, toasted sesame oil, minced ginger, minced garlic, and red pepper flakes to create the sauce.
Heat the avocado oil in a large non-stick skillet or wok over medium-high heat until shimmering.
Add the chicken to the skillet in a single layer and sear without moving for 3 minutes, then flip and cook for another 3-4 minutes until golden brown and cooked through.
Add the broccoli florets to the pan along with one tablespoon of water, then immediately cover with a lid to steam for 2 minutes until bright green and tender-crisp.
Remove the lid, pour the prepared sauce over the chicken and broccoli, and stir constantly for 1 minute until the glaze thickens and becomes glossy.