At some point, he earned the nickname 'The Grim' and in 985 fathered his son, Bodhe. 
In 997, with the help of Maol Chalvim II, Findlaech of Moray, Demona's Clan and Brooklyn (who had arrived in this time on his first TimeDancer adventure) he overthrew and killed Constantine III at the Battle of Rathveramoen. ("The Gate", "Tyrants", "Phoenix")
Kenneth then became King of Scotland, only to be overthrown and slain by Maol Chalvim eight years later. 
Kenneth III is a kind, approachable warm hearted man, truly a stark contrast to his nickname, the Grim. It has been pointed out that the nickname would have been more befitting of his cousin, Maol Chalvim II. It was Kenneth who first suggested that using gargoyles against Constantine's forces would be advantageous for the army of the Three Brothers (no doubt influenced by his ancestors' alliances with the creatures over the years). He seized the opportunity to ally with Brooklyn when the gargoyle was brought to him by Mary and Finella.
Real World Background
According to Greg Weisman, Kenneth III was originally written in "Avalon Part One", but was cut early on because the episode, "was just getting too damn complicated."  He was later introduced on Ask Greg in 1997 as a character in Once Upon A Time There Were Three Brothers..., long before Kenneth's canonical inclusion in the Gargoyles Universe in 2008.