Stir balsamic vinegar, lemon juice and soy sauce with salt, brown sugar, ground ginger, paprika, pepper and chilli flakes until the salt has dissolved. Stir in garlic, spring onions, sesame oil and peanut oil until well combined.
Pour marinade into a resealable plastic bag or glass bowl. Add salmon to marinade and gently toss to coat. Place into refrigerator and marinate 2 to 24 hours.
Prepare barbecue for medium-high heat.
Drain excess marinade from salmon fillets. Barbecue until firm and opaque, about 4 minutes per side.