Preheat your oven to 425°F. Pat the salmon fillets dry with paper towels and place them skin-side down on a baking sheet or oven-safe rack. Lightly brush with avocado oil and season generously with salt and pepper. Bake for 10-12 minutes until the salmon is cooked through and flakes easily with a fork. The salmon should be opaque and just beginning to flake at the thickest part. Remove from the oven and let cool slightly until you can handle it comfortably.
While the salmon cools, finely mince the red bell pepper and thinly slice the green onions. In a medium bowl, lightly beat the egg and set aside. Once the salmon is cool enough to handle, remove the skin by gently sliding a fork between the flesh and skin, then flake the salmon into bite-sized pieces using a fork. I like to remove the larger pin bones while flaking—it makes for a better texture in the finished cakes.
In a large bowl, combine the flaked salmon from Step 2 with the almond flour, minced red bell pepper, green onions, lightly beaten egg, smoked paprika, and lemon zest. Add 2 tablespoons of the bang bang sauce to the mixture for flavor and moisture. Gently fold everything together until just combined—don't overmix or the cakes will become dense. Divide the mixture into 4-6 equal portions and shape each into a 2-3 inch patty about ½ inch thick. I find it helps to chill the mixture for 15 minutes if you have time, as it makes the cakes hold together better during frying, but it's not essential.
Heat a large skillet over medium heat and add the butter and remaining avocado oil. Once the butter is melted and the pan is hot (a small piece of salmon mixture should sizzle immediately), carefully place the salmon cakes into the pan, working in batches if needed to avoid crowding. Fry for 3-4 minutes on the first side until golden brown and crispy, then gently flip and fry for another 3-4 minutes on the second side until golden. The cakes should be crispy on the outside while staying moist inside.
Transfer the cooked salmon cakes to a paper towel-lined plate to drain any excess oil. Arrange the cakes on a serving platter and drizzle generously with the remaining bang bang sauce or serve the sauce on the side for dipping. Serve warm while the cakes are still crispy on the outside.