Peel the mango and cut the flesh from the pit. Cut half of the mango into 1/2-inch pieces (about 1 cup) and transfer to a small bowl. Roughly chop the remaining mango and puree in a blender with the oil, vinegar, 2 tablespoons water, 1/2 teaspoon salt and a few turns of pepper.
Cut the thick center stem from each kale leaf and discard. Working in batches, mound a handful of kale on the cutting board and gather it together tightly. Slice crosswise to make very thin ribbons. Put the kale in a large bowl and toss with the mango dressing. Let stand at least 15 minutes and up to 45 minutes to wilt slightly.
Add the chopped mango, hearts of palm, rice and tomatoes; toss to coat. Season with salt and pepper. Top with the nuts.