Combine garlic, vinegar, oregano, parsley, honey and salt in a blender and blend until smooth. With the motor running, slowly add the oil and process until emulsified. Stir in the red chile flakes.
Place potatoes in a medium saucepan, cover with cold water and add 1 tablespoon of salt. Bring to a boil over high heat and cook until a paring knife inserted comes out with some resistance. Do not cook the potatoes all the way through because they will continue cooking on the grill. Drain well and when cool enough to handle, slice in half lengthwise.
Heat the grill to medium.
Brush the chicken and potatoes with oil and season with salt and pepper. Place the chicken on the grill, skin-side down and grill until golden brown and slightly charred, 6 to 7 minutes. Turn the chicken over and continue grilling until just cooked through, 5 to 6 minutes. A few minutes before the chicken has finished cooking, place the potatoes on the grill, cut-side down and cook until lightly golden brown, about 2 minutes. Turn over and continue grilling about a minute longer. Remove the chicken and potatoes to a platter and immediately drizzle with the roasted garlic-oregano vinaigrette. Let rest 5 minutes before serving. Garnish with oregano sprigs and parsley sprigs.