On the Internet, no one cares that you’re 13. That’s what Henry Kilpatrick discovered when he started his vintage-furniture retail site, Magic City Finds, in September 2011, at the dawn of his teen years. Mr. Kilpatrick, who is now 14 and lives in Birmingham, Ala., had no idea who Herman Miller was when he plucked a fiberglass armchair from his grandmother’s storage space, but one online search later, he knew he had a find. He plowed the $75 he made on that initial sale, along with some birthday money, back into furniture bought at estate sales and off Craigslist, including 20 more Eames chairs, which cycled through his parents’ garage. He mostly works on the weekends, as it is “tough to do schoolwork and business, and schoolwork comes first,” he said.