From 2002 to 2008, Kenny split time between playing for the Harbour Heat and earning his physiotherapy degree at the Auckland University of Technology. In December 2008, Kenny signed with the Hawke's Bay Hawks for the 2009 New Zealand NBL season. He became a staple with the Hawks, spending the next seven seasons with the team. On 29 December 2014, Kenny signed with Licher BasketBären of the German ProB. He appeared in 12 games for Licher, averaging 6.3 points, 4.3 rebounds, 4.2 assists and 1.2 steals per game. He returned to New Zealand in early April for the start of the 2015 NBL season. On 2 November 2015, Kenny signed with the Nelson Giants for the 2016 season. He joined the Giants on 23 March 2016. He appeared in 14 games for the Giants in 2016, averaging 8.6 points, 3.8 rebounds, 4.4 assists and 1.1 steals per game. On 20 September 2016, Kenny signed with the Hawke's Bay Hawks for the 2017 season, returning to the franchise after an injury-plagued 2016 season. On 1 April 2017, he recorded 22 points and 15 assists in the Hawks' 102–91 loss to the Wellington Saints. With the Hawks in 2017, Kenny averaged career-best numbers with 12.3 points, 4.5 rebounds and 7.5 assists over 15 games. On 14 November 2017, Kenny re-signed with the Hawks for the 2018 season. He returned to the Hawks for the 2019 season. On 21 April 2019, he recorded 15 assists and 10 rebounds to go with five points in a 105–95 win over the Southern Huskies. In June 2020, Kenny was acquired by the Otago Nuggets for the 2020 season. In his 19th season in the league, he won his first championship.
Kenny spent multiple seasons with the New Zealand Breakers as a practice squad player, but never got the callup to the top group. After impressing during the 2015 FIBA Oceania Championship, Kenny signed with the Perth Wildcats for the 2015–16 NBL season on 1 September 2015. On 6 November 2015, he scored a season-high 12 points in the Wildcats' 85–77 win over the Townsville Crocodiles. Kenny helped the Wildcats win the NBL Championship in March 2016 with a 2–1 grand final series win over the New Zealand Breakers. He appeared in all 34 games for the Wildcats in 2015–16, averaging 4.6 points, 2.1 rebounds and 1.3 assists per game, earning the club's Coaches' Award at the end-of-season MVP Ball. On 11 May 2016, Kenny re-signed with the Wildcats on a three-year deal. On 25 October 2016, Kenny was ruled out for three to five weeks with a groin strain. He returned to action on 17 November 2016 against the Sydney Kings and recorded a career-high five assists. Despite his minutes decreasing in 2016–17, Kenny remained a crucial figure in the rotation; his hard-nosed defensive aptitude, team-first mindset and likening for the big moment have made him a firm favourite of coach Trevor Gleeson. The Wildcats went on to win the NBL Championship in March 2017. In 30 games, he averaged 4.1 points, 1.8 rebounds and 2.0 assists per game. In January of the 2017–18 season, Kenny began playing in career-best form. With the turn of the new year, Kenny's scoring improved by nearly six points per game, while his percentage from beyond the arc spiked by almost 30 per cent. He recorded season highs in scoring, assists and rebounds from Round 14 onwards, while also knocking down a career-high four triples against the Sydney Kings on 19 January. He appeared in all 30 games for the Wildcats in 2017–18, averaging 5.2 points, 1.5 rebounds and 1.6 assists per game. On 22 April 2018, the Wildcats parted ways with Kenny after opting not to take the club option on his contract.
