Mbamba was born in Zimbabwe, and spent time with Hellas FC before he moved to Sweden to join the youth ranks of IFK Göteborg. He was vice-captain of the highly rated IFK Göteborg Under-19 team that won the Junior Allsvenskan Elite Southern Division in 2011 and reached the semi-finals of the Swedish Under-19 National Championships play-offs, losing to Kalmar FF 6-4 on penalties. He was also regularly part of the first-team squad and was an unused substitute in the 2010Svenska Supercupen defeat to AIK at Råsunda Stadium, though did not make an appearance in a competitive match. After the 2011 Allsvenskan season he was released, and subsequently spent two seasons with Qviding FIF of Division 1.
Norway
In 2014, he joined Norwegian side Medkila IL in the 2. divisjon, and scored two goals in 14 league games. He signed with Norwegian First Division side Alta IF in August 2014. However following their relegation, he went to Hamarkameratene ahead of the 2015 season. He damaged his cruciate ligaments in July 2015, and only returned to full fitness midway through the 2016 campaign. He recovered well, and in a reserve team match managed to provide an assist for all six goals in a 6–0 win over Kattem on 15 May. Hamkam manager Stein Arne Ingelstad said that Mbamba was a popular player who was "a little frustrating when he has not used his exceptional speed to pass defenders when he had the opportunity".
Port Vale
He signed with EFL League One club Port Vale in July 2016. He made his professional debut on 6 August, after coming on for Anthony de Freitas as a 57th-minute substitute in a 0–0 draw with Bradford City. He made 11 appearances across the 2016–17 season, and left the club in May 2017 after new manager Michael Brown agreed a settlement on the final 12 months of his contract.
Return to Sweden
Mbamba returned to Sweden and on 5 April2018 signed with Division 1 club Oskarshamns AIK. Oskarshamns finished second in the Södra table in the 2018 season and qualified to the promotion play-offs, but failed to reach the Superettan after losing out to Varbergs BoIS on away goals; Mbamba was a late substitute in both legs. He switched to divisional rivals Oskarshamns AIK in the off-season. On 28 January 2020, Mbamba signed with Division 2 side Assyriska BK.
International career
Mbamba was born in Zimbabwe to a Namibian father, and a Kenyan mother. He moved to Sweden at a young age, and represented the Sweden under-17s. In February 2019, Mbamba declared his intention to represent Kenya. He was granted a Kenyan passport the following month.
Style of play
Mbamba is versatile player who can play as a winger with tremendous pace and also as a box-to-box centre midfielder.