Heat the olive oil in a large heavy-bottomed pot or dutch oven over medium heat. Add the onions and fennel and sauté until translucent, about 8 minutes. Add the garlic, chili flakes, bayleaf, thyme, and oregano, then sauté for another 2-3 minutes. Add the tomato paste and stir until incorporated, then season lightly with salt and pepper. Go easy on the seasoning for now, as the seafood will add a significant amount of salt.
Add the white wine and clam juice, then bring up to a simmer and cook for about 5 minutes. Add the canned tomatoes and break them up a bit with a wooden spoon. Cover and simmer over low heat for 20 minutes.
Remove the lid and add the mussels and clams. Stir them around to coat with the broth, then cover and let cook for about 5 minutes. When they just begin to open, add the shrimp and king crab and toss around to coat, then lay the barramundi fillets on top. Season the barramundi with salt and pepper, then cover and cook for an additional 3-5 minutes, or until the shrimp and barramundi are opaque throughout.