Preheat the grill for indirect/medium-high heat.
Pat dry the ducks with paper towels, and then cut along the sides of the backbones using poultry or kitchen shears to remove them. Turn the ducks breast-side up, open the 2 sides as if you were opening a book and lay them flat. Break the breast bones by firmly applying pressure and pressing down (you may break a few rib bones in the process). Tuck the wing tips under the upper wings and place on a baking sheet or the Williams-Sonoma Steel Grill Roasting Pan.
Brush the ducks all over with olive oil and sprinkle lightly on both sides with the salt and some black pepper. Place the ducks skin-side up in the center of the grill and grill for about 2 hours.
Brush the Spicy Watermelon Glaze on the ducks, and then continue grilling until the juices run clear and the internal temperature of the thighs reaches 190 degrees F, 20 to 30 minutes longer, brushing with the glaze 2 more times.
Remove the ducks from the grill and brush with the Spicy Watermelon Glaze one last time and let rest 10 minutes. Cut the duck into halves or quarters and serve.
Run the watermelon through a food mill or juicer and collect the juice.
Melt the jelly in a small, heavy-bottomed saucepan over low heat, stirring occasionally so that it doesn't burn. Once melted, stir in the watermelon juice to combine, and then stir in the lime juice and zest. Mix in the red chile flakes, jalapeno hot sauce and salt. Taste and adjust the seasonings.
Use warm or let cool and transfer to a clean jar. The glaze will keep tightly covered in the refrigerator for up to 2 days.
Cook's Note: Juice an entire watermelon and use 4 cups juice for the Spicy Watermelon Glaze, and then drink the remaining 4 cups or use for another recipe, such as the Spiked Watermelon Aqua Fresca.