Cook the rice according to the package directions.
Meanwhile, heat a large wok or stainless-steel skillet over high. Add the canola oil, sesame oil, eggplant, and chicken to the wok and cook, stirring often, until evenly cooked and lightly browned, about 5 minutes. Add the garlic, ginger, red pepper, and scallion whites and cook, stirring often, until the scallions are tender, about 3 minutes. Add the teriyaki sauce and cook, scraping the bottom to loosen any browned bits and stirring often, until the vegetables are thoroughly cooked, about 1 minute. Stir in the scallion greens.
Serve hot over the cooked rice.