In a heatproof medium bowl, combine the carrot, cucumbers, radish & onion. In a small saucepan, bring the vinegar,sugar, salt, peppercorns and red pepper flakes to a boil. Reduce the heat and let simmer for 3 minutes, then remove from heat and let cool for 5 minutes. After 5 minutes, pour over the vegetables and toss to coat. Cover and refrigerate for at least 1 hour. Pickled veggies will keep in refrigerator for up to 1 week in the brine.