Gently toss tofu with 1 tablespoon soy sauce in a medium bowl; set aside.
Bring rice and 1 1/2 cups water to a boil in a medium saucepan. Cover; reduce heat to medium-low, and simmer until rice is tender and water has been absorbed, about 10 minutes. Set aside.
Heat olive oil and butter in a large skillet over medium heat. Add eggs, and cook, stirring, until just starting to set, about 30 seconds. Add reserved rice; stir to coat and break up any lumps. Reduce heat to medium-low, and add carrot, peas, and scallions. Cook until heated through, about 4 minutes. Add whole and ground flaxseed, remaining 2 tablespoons soy sauce, the sesame oil, and tofu; cook 5 minutes more. Season with pepper.