In a measuring cup, mix the soy sauce, sesame oil. brown sugar, ginger, and red pepper flakes. Pour half of the marinade into a large, zip-top bag. Add to the bag, seal, and shake to combine. Refrigerate at least 1 hour. Whisk the Hoisin sauce into the remaining marinade and set aside.
Heat the grill to high heat (about 500ºF).
Thread the marinaded chicken, zucchini, and mushrooms onto the skewers. Grill for 2-3 minutes per side, until grill lines appear and the chicken is mostly cooked through. Brush with glaze and cook another 1-2 minutes per side, or until cooked through.
Transfer to a plate a sprinkle with lime juice, chopped scallions, and crushed peanuts.