Slice the chicken breast into very thin strips against the grain.
In a small bowl, whisk together the tamari, honey, minced garlic, and grated ginger to create the marinade.
Toss the chicken strips in the marinade and let sit for at least 10 minutes.
Heat the toasted sesame oil in a large skillet over medium-high heat.
Add the sliced zucchini to the skillet and sauté for 2 minutes until tender-crisp, then transfer to a plate.
Add the marinated chicken to the same skillet and cook for 3-4 minutes until the edges are caramelized and the chicken is cooked through.
Push the chicken to one side of the pan and crack the egg into the empty space, scrambling it quickly until just set.
Stir the chicken, egg, and zucchini together with the cooked brown rice until heated through.
Garnish with sliced green onions, sesame seeds, and red pepper flakes before serving.