Combine kale, balsamic vinaigrette, and soy sauce in a bowl. Cover and marinate in the refrigerator for 1 hour.
Bring a large pot of water to a boil. Add yam pieces and cook until soft when pierced with a fork, about 15 minutes. Drain and cool; when yams can be handled, cut into cubes.
Warm black beans in a small saucepan over medium heat, 2 to 5 minutes.
Remove kale from vinaigrette mixture. Cook and stir kale with olive oil in a skillet over medium heat until dark green, about 2 minutes.
Place half the yams on each tortilla and top yams with black beans, kale, and feta cheese. Fold bottoms of tortillas partially over filling and roll to wrap the filling in the tortillas.
