Drying the Chicken: (should be done at least the night before) Rub or pat salt onto breasts, legs and thighs of chicken.
Place chicken in a large resealable plastic bag. Set open bag in a large bowl, keeping chicken breast side up.
Chill for up to 2 days, but at least 8 hours.
To Roast Chicken: Arrange a rack in upper third of oven; preheat to 500°F. Prepare fresh pomegranate juice, if necessary.
Set a wire rack in a large heavy roasting pan. Remove chicken from bag. Pat dry with paper towels (do not rinse). Place chicken on prepared rack, breast side up.
Use half the thyme and rosemary bunches to stuff in the cavity and the other half to season the outside of the bird before roasting. Loosely tie legs together with kitchen twine and tuck wing tips under. Brush chicken all over with some olive oil.
Roast chicken, brushing with olive oil after 15 minutes, until skin is light golden brown and taut, about 30 minutes. Reduce oven temperature to 350°F. Remove chicken from oven and brush with more oil. Let rest for 15–20 minutes.
POM Vinaigrette: While chicken is resting, pour 2 cups of pomegranate juice into a non-reactive pan and reduce by half. Pour reduced pomegranate juice into a chilled bowl, along with julienned shallots, whisking in 2 tablespoons chili flakes, 1 cup extra-virgin olive oil and kosher salt to taste.
Salad: Cut avocados in half, discard the pit, and scoop the flesh out. Cut into ½" cubes and place in bowl with POM Vinaigrette. Add the arugula and lettuces; lightly mix.
To Finish: Return the chicken to the oven and roast for 40–45 minutes, until the skin is golden brown and a thermometer inserted into the thickest part of the thigh registers 165°F. Let rest for 20 minutes, then carve.
Place dressed avocado and greens onto a plate and put carved chicken on top. Sprinkle the feta onto chicken and salad, and lightly spoon any leftover dressing onto chicken.