Whisk lime juice, rice vinegar, cilantro, ginger, garlic, honey, sesame oil and pepper flakes in a small bowl. Prepare rice noodles according to package directions; drain and quick chill in a bowl of ice water. Once well drained, toss noodles in a large bowl with carrot, scallion, cucumber and peanuts and pour dressing over top. Mix well. To serve, place into serving bowls, and top with a heap of beets.