Kabongo started playing for hometown club Albertslund IF before signing a youth contract with Brøndby IF. During his time in the youth teams, Kabongo was a part of the under-17 team that won the championship and the domestic cup. On 31 August 2017, Kabongo moved to second division club Fremad Amager on loan until 1 January 2018. He made his first-team debut for Fremad on 3 September, coming on as a substitute for Heini Vatnsdal in the 82nd minute of a 1–0 win home win against Esbjerg fB.
After returning to Brøndby from his loan spell, Kabongo saw playing time in the team’s pre-season friendlies, being in the starting lineup in a match against Shakhtar Donetsk. Kabongo made his official debut for Brøndby in the first match of the 2018–19 Danish Superliga season, starting in a 2–0 away win over Randers FC and playing the entire match.
On 16 August 2018, Kabongo made his UEFA Europa League debut, starting in a 2–1 home win over Spartak Subotica. His debut was short-lived, however, as he was sent off in the 15th minute for a professional foul on Dejan Đenić. On 26 August 2018, in a 2–1 win over Vendsyssel FF, Kabongo was sent off again, this time for a 92nd minute foul on Sander Fischer, resulting in a penalty and Kabongo being shown a second yellow card. On 22 April 2019, in a match against FC Midtjylland, Kabongo suffered a cruciate ligament tear and was substituted in the first half. The initial prognosis suggested that he would miss 12 months.
On 5 March 2020, Kabongo, alongside several other Brøndby personnel, was placed in home quarantine after having met with former Brøndby-player Thomas Kahlenberg, who had tested positive for SARS-CoV-2 in the early stages of the COVID-19 pandemic in Denmark. Kahlenberg had been infected at a birthday party in Amsterdam, the Netherlands. Kabongo made his comeback in football on 21 May 2020 in a friendly against Lyngby.