Bring an inch or two of water to a boil in a saucepan fitted with a steamer basket. Add potatoes to the steamer, cover and cook until the potatoes are just barely tender when pierced with a fork, 7 to 9 minutes. Remove the steamer from the saucepan.
Heat oil in a large non-stick skillet over medium-high heat. Add potatoes and cook, stirring often until they are starting to brown, 6 to 8 minutes.
Meanwhile, stir vinegar, mustard, honey, salt and pepper together in a small dish.
Stir the sauce, sausage and figs into the potatoes. Top with kale and cover. Cook, stirring to mix in the kale as it wilts and continue cooking until the kale is completely wilted, the figs and sausage are hot and the vinegar mixture forms a glaze over the potatoes, 3 to 4 minutes.