In a large bowl, combine the chicken, 1 tablespoon soy sauce, 1 teaspoon apple cider vinegar, and 1 teaspoon granulated sugar. Set aside while you prep the remaining ingredients.
In a small bowl or large liquid measuring cup, stir together the remaining 3 tablespoons soy sauce, remaining 1 teaspoon apple cider vinegar, remaining 1 teaspoon sugar, the ginger, garlic, water, cornstarch, and red pepper flakes. Set aside.
Trim off the ends of the zucchini. Cut in half lengthwise, then place the flat, cut sides on the counter. Slice crosswise into 1/4-inch thick half moons. Thinly slice the onion.
In a wide skillet, heat 1 tablespoon of the olive oil over medium-high heat. Once the oil is hot, add the chicken and its marinating liquid. Saute until the chicken is golden brown on the outsides and fully cooked through, about 3 to 4 minutes. Remove to a plate.
Heat the remaining 1 tablespoon oil. Add the onion. Cook until tender and beginning to brown, 4 to 5 minutes.
Give the sauce one more stir, then add it to the pan. Let cook 30 seconds, then add the sliced zucchini. Cook just until the zucchini begins to soften, about 3 minutes more.
Remove from the heat, then stir in the reserved chicken. Serve hot with a sprinkle of sesame seeds and green onion as desired.
TO STORE: Leftovers can be stored in an airtight storage container in the refrigerator for up to 4 days.
TO REHEAT: Gently rewarm zucchini stir fry in a large skillet on the stovetop over medium-low heat. You can also reheat this dish in the microwave.
TO FREEZE: Place leftovers in an airtight, freezer-safe storage container in the freezer for up to 3 months. Let thaw overnight in the refrigerator before reheating.