Kennelly made his debut on the inter-county scene at the age of seventeen when he was picked on the Kerry minor team. He had two championship seasons with the minor team, however, he was a Munster runner-up on both occasions. Kennelly subsequently joined the Kerry under-21 team, winning two All-Ireland medals as a substitute in 1973 and on the field of play in 1975. By this stage he had also joined the Kerry senior team, making his debut during the 1974-75 league. Over the course of the next ten years, Kennelly won five All-Ireland medals, beginning with a lone triumph in 1975 before a record-equalling four championships in-a-row from 1978 to 1981. He also won nine Munster medals, three National Football League medals and claimed back-to-back All Stars in 1979 and 1980. He played his last competitive game for Kerry in February 1984, but remained on the panel for the subsequent provincial championship.