Kaminski started his archery career at the age of six near his hometown of Elma, New York, focusing on compound shooting at a Junior Olympic Development Club. By the age of 15, he focused his attention on recurve archery so he could one day compete in the Olympics. At the 2012 Summer Olympics he competed for the U.S. in the Men's team event and won a silver Olympic medal along with his teammates Brady Ellison and Jacob Wukie. At the 2016 Summer Olympics, he once again competed for the United States in the Men's team event and took home another silver Olympic medal, alongside teammates Brady Ellison and Zach Garrett.