Toast the dry ramen noodles in a skillet over medium heat until golden brown, stirring frequently, about 10 minutes. Spread the noodles into a large mixing bowl to cool; set aside. Make the dressing by whisking the vinegar, soy sauce, garlic, ginger, red pepper flakes, and black pepper together in a small bowl. Whisk in the peanut oil and sesame oil until blended and thick.
Combine the peas, jiciama, water chestnuts, celery, green onions, and cashews in the bowl containing the toasted noodles. Pour the dressing overtop, and toss to mix immediately prior to serving.