Combine greens, herbs and scallions. Slice the seeded, peeled half melon into thin strips lengthwise then halve the slices across into thin planks about 2 1/2-inches long; combine the sliced melon with the greens. Cut the prosciutto slices lengthwise to make 2 ribbons from each slice; reserve.
Heat a large, nonstick or cast-iron skillet over medium-high heat.
Butterfly chicken pieces and pound very thin; season with salt, pepper and a little sprinkle of chili flakes. Add oil to pan, 2 turns, and crushed garlic. Cook 2 pieces of chicken 2-3 minutes on each side to golden; remove to a warm platter and cover. Add more oil to the pan, if necessary, and repeat with remaining chicken. Add wine to pan and deglaze; add juice of 1 lemon and swirl in butter to finish sauce.
Dress greens and melon with juice from remaining lemon, to taste, and drizzle salad with a little EVOO. Season with salt to taste.
To serve, place chicken on plates, spoon a little wine and lemon sauce over them and top with 6 loosely mounded ribbons of prosciutto and then some of the greens and melon salad.