For the turkey burgers: Thoroughly combine the turkey, scallions, garlic, paprika, cumin and red pepper flakes in a medium bowl; sprinkle with salt and pepper. Form the mixture into four 3/4-inch-thick patties and season lightly with salt and pepper.
For the feta yogurt sauce: Combine the yogurt, feta, dill, garlic and lemon juice in a small bowl. Season lightly with salt and pepper.
Heat a grill or grill pan over medium-high heat. Toast the English muffins, cut-side down, until golden and set aside. Spray the burgers on both sides with cooking spray and grill until browned and entirely cooked through, 4 to 6 minutes per side. Place each burger on the bottom piece of an English muffin, top with the yogurt sauce and sandwich the top piece of an English muffin.