In 2008, the Boston Red Sox drafted Kelly with the 30th overall pick. After a trade to the San Diego Padres, he made his MLB debut in 2012. However, in March of 2013, he was diagnosed with micro tears in his UCL and underwent a reconstruction. In 2015 he was traded to the Atlanta Braves. After a cup of coffee in the big leagues, he was released by the Braves brass. Subsequently, he was signed by the Chicago Cubs but released mid-summer. In December 2017, Kelly came to the ARMory looking to up his game. After several months of remote training, he signed with the San Francisco Giants. Once again, in 2018, Kelly made an appearance in the big leagues with the San Francisco Giants. His hard work yielded great results and in 2019, Kelly signed with the LG Twins of the KBO. He went on to post stellar numbers in 2019 and 2020.