Cut the white and light green parts of the scallions into 1 1/2-inch pieces; set aside. Chop the dark green parts and transfer to a blender. Add the dill, parsley, olive oil, 3 tablespoons water and 1/2 teaspoon salt and puree until smooth. Stir in the red pepper flakes. Remove 2 tablespoons of the puree to a small bowl for the sauce; refrigerate until ready to use. Transfer the remaining puree to a large bowl. Add the chicken and toss to coat. Let marinate in the refrigerator at least 4 hours or overnight.
Soak 8 wooden skewers in water for 30 minutes to prevent scorching. Preheat a grill to medium. Thread 2 chicken thighs onto double skewers, placing lemon wedges and scallion pieces between the thighs; season the kebabs generously with salt and pepper. Oil the grill grates. Grill the kebabs until the chicken is lightly charred and cooked through, 8 to 10 minutes per side. Transfer to a cutting board and let rest 5 minutes.
Mix the yogurt with the reserved scallion puree and season with salt. Cut the chicken in half to separate each pair of skewers. Squeeze the grilled lemon over the chicken; serve with the yogurt sauce.