With a sharp knife, score the fat of the duck breasts in a cross-hatch pattern through the fat, down to the meat but not into the meat. Season generously with salt.
Preheat the oven to 350 degrees F.
Put about a tablespoon of olive oil in a large saute pan over low heat and schmear it around to coat the bottom of the pan. Arrange the duck breasts, skin side down, in the pan. Be sure that the duck fits in the pan comfortably and is not crowded. Slowly render the fat from the duck breasts. This needs to be done s-l-o-w-l-y, otherwise the fat with be sealed into the skin and will not render out. The idea is to make crispy duck skin. This process will take about 30 minutes or so. As the fat builds up in the pan, remove it, but SAVE IT! It will be used to saute the kale later.
When the fat has rendered from the duck breast, turn the heat to medium-high and brown both sides of the duck breast. When the duck is browned on both sides, move it to a sheet pan and put it in the preheated oven to cook it to medium rare, about 7 to 8 minutes. Remove the duck from the oven to a cutting board and let it rest for about 10 minutes before slicing.
Add the clementine juice and segments to the saute pan and scrape up the brown bits that cling to the bottom of the pan. When the juice has reduced by a little more than half, add half of the chicken stock, the thyme and season the whole shootin' match with salt. Continue to cook until the stock has reduced by half, then add a little more of the chicken stock. Continue to reduce the stock and turn the heat off when it gets to a sauce-like consistency. Taste for seasoning and add salt, if needed.
While the sauce is reducing and the duck is resting, add some of the reserved duck fat to a large saute pan. Add the garlic cloves and bring to a medium-high heat. When the garlic is golden brown and aromatic, remove it from the saute pan and discard it. Toss in the prepared kale and season with salt, to taste. Add some of the reserved chicken stock to help steam the greens. Saute the greens until they are wilted but still vibrant looking. Taste for seasoning.
Divide the greens among 4 serving plates. Slice each duck breast and fan the slices over the kale. Spoon some of the sauce on and around the duck. Garnish with the supremed clementines and the pomegranate seeds.