Combine chicken thighs, 2 teaspoons kosher salt, pepper, rosemary, thyme, oregano, red pepper flakes, cayenne, garlic, lemon juice, and ¼ cup olive oil in a large mixing bowl. Toss very thoroughly to combine, making sure the chicken thighs are completely and evenly coated with the marinade.

Wrap in plastic and marinate in the refrigerator for 6 to 12 hours.

Preheat the oven to 475 degrees F (245 degrees C). Line a baking sheet with foil and grease generously with olive oil.

Meanwhile, halve potatoes lengthwise; slice each half into 3 equal pieces. Dice into cubes and set aside.

Transfer chicken thighs to the prepared sheet pan smooth-side up, spacing evenly. Reserve any excess marinade in the bowl.

Add the potatoes to the bowl the chicken was in, along with a splash of olive oil and a large pinch of salt. Toss well to coat evenly. Scatter potatoes onto the chicken and distribute as evenly as possible in between the chicken thighs to fill any empty spaces.

Roast in the center of the preheated oven until the chicken is cooked through, about 35 minutes. Remove chicken to a plate or dish and cover. Chicken can be cut into bite-sized pieces if desired.

While chicken and potatoes are cooking, whisk red wine vinegar, olive oil, lemon juice, salt, and pepper together for dressing. Taste and adjust vinegar or oil as needed. Whisk in parsley and oregano.

Toss the potatoes in the chicken fat and pan drippings, and return to the oven until well browned and crusty, 10 to 15 minutes. Let potatoes rest for a few minutes before removing them with a spatula.

To make bowls, toss together cucumbers, tomatoes, red onions, feta cheese, chicken, potatoes, and dressing until evenly combined. Serve on top of a bowl of greens.