Season the halibut fillets with salt and pepper.
In a large skillet with a lid (non-stick is preferable), heat 2 tablespoon of the oil over medium-high heat.
Add the halibut and sear until golden brown on one side, about 2 minutes (you may need to do this in batches). Transfer to a plate.
Warm the remaining 2 tablespoons of oil over medium heat.
Add the onion and cook until soft, about 4 minutes.
Add the tomatoes, garlic, pepper flakes, 1/2 teaspoon salt, 1/4 teaspoon of pepper, and cook for about 1 minute.
Add as much kale as will fit in the pan.
As the kale wilts, continue adding the rest. You may need to add a splash of water (about 1 tablespoon), if the pan gets too dry.
Cook until the kale is just wilted, about 2 minutes.
Stir in the beans and 1/2 cup of water. Bring to a simmer, cover, and cook until the kale is very tender and the liquid has thickened, about 8 minutes.
Taste and add more salt and pepper, if needed.
Nestle the halibut fillets in the kale, browned side up, cover, cook until the fish is opaque throughout, about 4 minutes.
Drizzle with a little oil and serve with lemon wedges.