Kusunga began his playing career with Servette, having progressed through the club's youth team. He made 17 appearances for the club in the Swiss 1. Liga, scoring once. He made a further 68 Challenge League appearances, scoring five times during his five-year tenure with the club. In May 2010, ahead of the 2010–11 Swiss Super League season, Kusunga signed for Swiss Super League side FC Basel, and was handed the number 21 shirt on his arrival. Kusunga made his debut for Basel on 20 July 2010, coming on as a 46th-minute substitute in the club's 3–2 home win against FC Zürich. At the end of the 2010–11 Swiss Super League season Kusunga won the Super League Championship title with Basel and at the end of the 2011–12 season he won the Double, the League Championship title and the Swiss Cup, with Basel.
Kusunga signed for Oldham Athletic until the end of the 2013–14 season on 2 September 2013, with the option of extending the deal until the summer of 2015. Kusunga was recommended to the Latics by Oldham legend, Joe Royle, his son Darren's agency heard about the player whilst scouting in Switzerland. Kusunga was offered more lucrative deals to clubs in Israel and Bulgaria but the sharp tongued Joe Royle stepped in along with his son to secure a deal with Lee Johnsons side. Kusunga scored his first goal for the club in the first round of the FA Cup, giving the Latics the lead against Wolverhampton Wanderers. Kusunga scored his first league goal on 25 January 2014 and it turned out to be a goal that will be remembered by Latics fans for many years to come, Oldham were 3–0 down against Peterborough United at half – time and many of the Latics faithful thought that the game was all over, with a minority of the fans even leaving at half – time, however, after the interval, the Latics got the score back to 3–2 and looked to have the momentum on their side to mount a comeback, however, they conceded again and the chances of that happening seemed to disappear with the scoreline at 4–2 but the Latics picked themselves up and scored straight away to make it 4–3 and the comeback was back on. Then in the dying minutes of the game, the Latics got a penalty and scored it to make it 4–4. And then something happened to turn the game into one of the most memorable games in Oldham's history, in the last seconds of the game, deep into injury time, Kusunga scrambled a shot into the back of the net from a corner in the 96th minute and Oldham won the game 5–4 after being 3–0 and 4–2 down during the game. The one – year contract extension option that the club had on Kusunga was exercised, extending his contract till the end of the 2014–15 season. On 24 April 2015, Kusunga was released by Oldham.
C.F. União
After being without a club for 10 months, Kusunga signed a deal with C.F. União in the Portuguese Primeira Liga.
Kusunga, who as a free agent was able to sign outside of the transfer window, signed for Scottish Premiership club Dundee on 2 February 2018. He replaced Jack Hendry, who had been sold to Celtic on 31 January. He was released by Dundee at the end of the 2018-19 season.
Cova da Piedade
On 17 December 2019, Kusunga joined Portuguese LigaPro club C.D. Cova da Piedade on a free agent.
International career
In 2009, Kusunga was called up twice for the Switzerland U21 side, but was an unused substitute in both games. He has, however, since committed his international future to Angola, and played a friendly for them in the buildup to the 2013 African Cup of Nations.
