Fill a large pot with 1-inch water and fit with a steamer basket. Bring to a simmer. Place the potatoes in the steamer basket, cover, and steam until very tender, 15 to 18 minutes
Meanwhile, whisk together the lemon juice, thyme, crushed red pepper, 2 tablespoons of the oil, and ¼ teaspoon salt in a small bowl.
Heat 1 tablespoon of oil in a large nonstick skillet over medium-high heat. Season the halibut with ½ teaspoon salt and ¼ teaspoon black pepper. Cook until opaque throughout, 3 to 5 minutes per side.
Heat the remaining tablespoon of oil in a separate large skillet over medium-high heat. Add the shallot and cook, tossing occasionally, until tender, 2 to 4 minutes.
Add ¼ cup water and as much kale as will fit and cook, tossing frequently and adding more kale when there is room, until tender, 6 to 8 minutes. Season with ¼ teaspoon each salt and black pepper.
Serve the halibut with the potatoes and kale. Drizzle with the lemon-thyme vinaigrette.