Combine the vinegar, sugar, pepper flakes, and salt in a bowl, and add the cucumber slices.
Cover the bowl with plastic wrap and allow to marinate for at least 30 minutes.
Place the salmon chunks, smoked salmon, egg, spinach, lemon zest, and black pepper in a blender and pulse four to five times until just combined. The mixture should be chunky.
Form the mixture into four patties and set aside.
Heat the oil in a skillet over medium-high heat. Carefully slide the patties into the heated skillet and cook for about 4 minutes on each side or until heated through.