Kennedy came through the youth system at Rangers On 15 June 2018, Kennedy signed a three-year contract with the club. He made his first-team debut for Rangers on 17 January 2020 in a Scottish Cup match against Stranraer at Ibrox Stadium.
In late September 2020, it was reported by the Daily Record that Kennedy was being chased by multiple clubs including Sheffield United, Manchester City, Roma and Bayern Munich due to a contract dispute with Rangers. He played against Inverness CT in a Tunnocks Caramel Wafer Challenge cup game at the Caledonian Stadium in season 2019/2020. In October 2020 he was loaned to Inverness Caledonian Thistle in the Scottish Championship. This was a six month deal. Kai scored his only goal for Inverness on 4th December at Palmerston in the Scottish Championship. Kai's loan spell came to an end in January 2021. His final game for Inverness was as a substitute against Dunfermline in a 1-1 draw at the Caledonian Stadium on the 29th December when he came on at the interval to replace the injured Aaron Doran. Kai has renewed his contract at Rangers and has gone on loan to Raith Rovers for the rest of season 20/21.