Prepare the rice according to package directions, adding the cinnamon stick with the water. Fluff the rice, discard the cinnamon stick and set aside to cool.
Toss the shrimp with half of the ginger, 1 tablespoon of the sake, the vinegar and pepper flakes in a medium bowl. Let marinate 10 to 15 minutes. Mist a large nonstick skillet with cooking spray and heat over medium-high heat until very hot. Add the shrimp with the marinade and cook, stirring, until just opaque, 2 minutes. Transfer to a large plate and set aside.
Mist the same skillet and return to medium-high heat. Lightly beat the eggs and egg whites and add to the skillet. Cook until scrambled, breaking up with a spatula and transfer to the same plate as the shrimp.
Return the skillet to medium-high heat, mist with nonstick spray and add the snow peas, carrots, garlic, onions and remaining ginger. Cook, stirring, until softened and crisp-tender, 5 minutes. Transfer to the same plate as the shrimp and eggs.
Return the skillet to medium-high heat and add the vegetable oil. Add the cooled rice, toss with the oil and pack in the skillet in a firm layer. Cook, without stirring, until the bottom of the rice is browned and crusty. Stir the rice and pack it in another layer. Repeat the process until the rice is well toasted and browned, and stopping if the rice seems to be getting dry. Add back the shrimp, eggs and vegetables along with the remaining 1 tablespoon sake and soy sauce and toss well to combine. Remove from the heat and top with the sliced scallions.