Combine the salmon with a lightly beaten egg, bread crumbs, lemon zest and juice, dill, garlic, Dijon mustard, Worcestershire sauce, and red pepper flakes. Mix well.
Season with salt and pepper and stir the mixture until well-combined.
Heat the oil in a non-stick or cast-iron skillet. Cook the patties on medium heat until crispy and brown, or about 3-5 minutes on each side.
Heat the hamburger buns. Serve the patties on the buns with the fixings. Enjoy!