In a medium bowl, whisk together the soy sauce, brown sugar, olive oil, minced garlic, ground ginger, black pepper, and red pepper flakes (if using) until the sugar is dissolved.
Place the salmon fillets in a large resealable plastic bag or a shallow dish. Pour the marinade over the salmon, ensuring it is well coated. Seal the bag or cover the dish and refrigerate for at least 30 minutes, or up to 2 hours for more flavor.
Preheat your grill to medium-high heat. Lightly oil the grill grates to prevent sticking.
Remove the salmon from the marinade and discard the marinade. Place the salmon skin-side down on the grill.
Grill the salmon for about 6-8 minutes per side, or until it flakes easily with a fork and reaches an internal temperature of 145°F.
Remove the salmon from the grill and let it rest for a few minutes. Garnish with chopped green onions and serve with lemon wedges.