Flemming played in the youth departments of ZSGOWMS, RKSV Pancratius and Ajax.[2] He made his professional debut for Jong Ajax on 1 September 2017 in a game against Jong PSV and scored on his debut.[3] Flemming made 25 appearances during the 2017–18 season and won the Eerste Divisie title with Jong Ajax.[4]
PEC Zwolle
On 2 May 2018, Flemming signed a three-year contract with PEC Zwolle, starting from 1 July 2018.[5] There he made 28 appearances and six goals in his first season.[6] His most notable performance came in the KNVB Cup against De Graafschap, where he scored four goals in a 5–2 victory.[7]
Loan to NEC
On 2 September 2019, Flemming was sent on loan to NEC for the 2019–20 season, who were competing in the second-tier Eerste Divisie.[8] On 13 September, he made his debut in the 2–2 away draw against FC Den Bosch.[9] He scored his first two goals for NEC on 27 September, when the club drew 3–3 against Go Ahead Eagles.[10] With 13 goals, he became club top scorer of NEC for the 2019–20 season.[11] As the season ended, he returned to PEC Zwolle.[12]
Fortuna Sittard
On 26 August 2020, Flemming signed a four-year contract with Eredivisie club Fortuna Sittard.[13] He made his debut on 12 September in a 2–0 away loss to Twente.[14] On 26 September, he scored his first two goals in a 3–3 home draw against AZ, one of them coming deep into injury time to secure the one point for Fortuna.[15][16] He finished the season with 35 appearances, in which he scored 25 goals,[6] as Fortuna finished in 11th place.[17]
Millwall
On 25 June 2022, Flemming joined Championship club Millwall on a three-year contract for a fee of £1.7m rising to £2.5million.[18] He made his competitive debut for the club on 30 July, the opening day of the season, replacing George Honeyman in the 76th minute of a 2–0 home victory against Stoke City.[19] On 17 September, he netted his debut goal for the Lions, breaking the deadlock in the 14th minute with a header from Scott Malone's cross. The ball deflected off keeper Daniel Grimshaw and secured his team's lead in a 2–1 victory against Blackpool.[20] He secured his second goal on 5 October during a match against Rotherham United from a long-distance strike.[21] Just three days later, he achieved his first brace for Millwall, propelling them to a 2–0 victory against Middlesbrough at The Den.[22] He continued his impressive form the following week, on 15 October, by netting the decisive goal that secured a 2–1 away win against Bristol City. This marked Flemming's fifth goal in five consecutive games.[23] On 12 November, Flemming scored his first hat-trick for the club, once again proving decisive in a 4–2 away victory against Preston North End.[24] He concluded the season with 15 goals in 44 appearances across various competitions, securing the position of the team's second-highest goalscorer, behind only Tom Bradshaw.[6] Millwall finished eighth in the league, narrowly missing the playoffs by just one point behind sixth-place Sunderland in the play-offs.[25] In recognition of his contributions, Flemming was honoured as the Millwall Player of the Season in May 2023.[26]