Rinse salmon and place in a container with a lid. Pour in teriyaki marinade; cover container. Chill in the refrigerator for 30 minutes or up to 2 hours.
Heat olive oil in a large skillet over medium heat. Add onion; saute until soft, 2 to 4 minutes. Stir in tomatoes and mushrooms. Cook until softened, 2 to 3 minutes. Add vinegar, soy sauce, lemon juice, and hot pepper sauce. Mix in turmeric, cinnamon, and cumin until fragrant, 2 to 3 minutes.
Move vegetables to the sides of the skillet and place salmon in the middle. Cook for 2 1/2 minutes; turn over and cook for another 2 1/2 minutes. Break salmon apart with a spoon and mix with the vegetables. Add almonds, sunflower seeds, flax seeds, and cranberries. Stir in goat cheese.
Heat naan bread one at a time in a skillet over medium-high heat. Toast 15 seconds; turn and toast another 15 seconds. Serve with salmon stew.
