Mix the water, soy sauce, kosher salt, green onions, garlic, ginger, black pepper, and pepper flakes in a large bowl. Stir well until the salt completely dissolves. It might take a few minutes. To save time, dissolve the salt in about a cup of hot water and let it cool completely before adding it to the brine.
Add tuna steaks to the brine, or put them in a large ziplock bag and pour the brine over them until fully submerged. Add more brine as needed.
Seal the bowl with plastic wrap or seal the ziplock bag and refrigerate for 1-3 hours, depending on the steak's thickness. Avoid brining for too long as tuna is delicate and can get overly salty and fall apart when smoking.
Remove the tuna steaks from the brine, discard excess particles, and gently pat them dry with paper towels. If time permits, let the tuna air-dry in the refrigerator for an hour or two to form a pellicle (a film that absorbs the smoke better and keeps the fish moist).