Kabamba was a sprinter when young, but opted to play football instead. He joined Uxbridge in 2011 after scoring 13 goals forHayes & Yeading United's under-18 team. He impressed enough with the reserve squad to grant a debut on 22 November in a Southern League Cup 3–1 defeat at Northwood. Kabamba left Uxbridge in October 2013 and signed for A.F.C. Hayes. After a goalscoring debut against North Greenford United, he only scored one further goal for the club, in a 2–1 away loss against Potters Bar Town, before leaving in November. He subsequently moved to Burnham before the window break, and started to score in a regular basis. On 30 September 2014 Kabamba scored five goals in a game including a hat-trick in the opening 10 minutes as Burnham beat Bideford 5–1 in the Southern League. On 5 December 2014, he was loaned to Hemel Hempstead Town until the end of the season.
On 18 January 2017, Kabamba signed an 18-month contract with League Two club Portsmouth with the option of a 12-month extension. He made his debut for the club on 18 March, replacing Noel Hunt in a 3–0 away defeat to Stevenage. On 31 August 2017, Kabamba signed for Colchester United until January 2018, becoming the fifth player to enter Colchester on deadline day. He made his Colchester debut on 9 September in their 3–1 win against Crawley Town. After failing to score in ten appearances for Colchester, he returned to his parent club on 14 December. On 5 January 2018, Kabamba joined National League side Aldershot Town on loan for the remainder of the campaign. On 9 May, Portsmouth announced that his contract, which would expire on 30 June, would not be renewed.
On 14 June 2018, Kabamba signed for National League newcomers Havant and Waterlooville and has made 32 appearances and scored 6 goals across all competitions.
On 18 January 2019, in a return to full-time professional football, Kabamba signed on loan for fellow national league side Hartlepool United, scoring 5 goals in his first 4 starts. He finished his loan spell with 7 goals in 17 National League appearances, including a goal in a 3–2 win over Salford City F.C. on the final game of the season which ended their opponents' title run. Kabamba signed a permanent deal on 13 May 2019.
Kilmarnock
Kabamba signed for Scottish Premiership club Kilmarnock on a one-and-a-half year contract on 17 January 2020. He scored on his debut, coming off the bench in a 6–0 win against Queen's Park in the Scottish Cup.
