For the Horseradish Sauce:
Whisk together sour cream, mayonnaise horseradish, chives, vinegar, garlic, and salt in a small bowl; taste, and add more seasoning, as desired. Chill before using, at least 30 minutes. (Can be made up to 2 days ahead; store refrigerated in an airtight container.)
For the steak:
Fill a medium saucepan with water, a large pinch of salt and the potatoes, and bring to a boil over high heat. Cook until knife tender, about 20 minutes. Drain then set aside to cool while you prepare the steak. (Can be made up to 2 days ahead of time. Store cooked potatoes refrigerated in an airtight container until ready to use.)
Meanwhile, heat 1 tablespoon of the oil in a large cast iron or other heavy-bottomed skillet over medium-high heat. Season steak all over with salt and pepper. When the oil comes off the skillet in wisps, over medium-high heat until cooked to desired doneness, about 4 minutes per side for flank steak. Transfer meat to a plate and let rest for 5 minutes before slicing.
While steak rests, slice fingerling potatoes in half lengthwise, season with salt and pepper, and toss with half of the remaining oil. Divide greens and potatoes among serving dishes, drizzle with remaining oil and squeeze half of the lemon over the top. Thinly slice steak and place on serving dishes with a dollop of horseradish cream then pass the lemon and additional sauce on the side.