Kachunga spent his early career in Germany with
Borussia Mönchengladbach,
VfL Osnabrück,
Hertha BSC and
SC Paderborn. Following Paderborn's relegation, he moved to
FC Ingolstadt 04 in June 2015. He was the club's record signing, at a transfer fee of €1.7 million. He made his debut for them on 6 August 2016, scoring the first goal in a 2–1 win over
Brentford. On 22 March 2017, Huddersfield paid Ingolstadt £1.1 million to turn Kachunga's loan deal into a permanent transfer. In December 2017 he was ruled-out for three months due to injury. He was released by Huddersfield at the end of the 2019–20 season. On 2 September 2020, he was signed by
Sheffield Wednesday on a free transfer. He made his debut coming off the bench against
Cardiff City on the opening day of the season. He scored his first goal for Wednesday in a 2-0
EFL Cup win against
Rochdale on 15 September 2020. On 20 May 2021, it was announced that he would leave Sheffield Wednesday at the end of the season, following the expiry of his contract. On 6 August 2021, he signed for
Bolton Wanderers. He made his debut a day later as a late substitute against
Milton Keynes Dons and provided an assist for
Alex Baptiste in the 95th minute, rescuing a point for Bolton in a 3–3 draw. His first Bolton goal came on 7 November in a 2–2 draw against
Stockport County in the
FA Cup. On 2 April, he started in the
2023 EFL Trophy Final. He scored the third goal, with the Final against
Plymouth Argyle eventually ending with a 4–0 Bolton win. On 23 May the club confirmed that Kachunga would be leaving at the end of his contract in June. On 1 August 2023 he signed for
Cambridge United. ==International career==