Professor Kennedy joined the teaching staff of the Department of Geology and Mineralogy in 1967, became curator of the Museum's Earth Collections in 1976, and was Director of the Museum between 2003 and 2010. He has received numerous awards, including the Prestwich Medal of the Geological Society of London, the Neville George Medal of the Glasgow Geological Society, a Gold Medal of the Linnean Society, and the inaugural Gold Medal of the Paleontographical Society.
His research interests lie in the Cretaceous period; currently he is focused on ammonite faunas from the UK, Germany, Kazakhstan, Uzbekistan, Texas (USA), Nigeria, KwaZulu-Natal (South Africa), Madagascar, Nigeria and south India.
He remains actively engaged in research on, and curation of, the Museum's collections.