Kiwomya was born on 20 May 1996 in Sheffield. He attended Notre Dame High School, Sheffield before joining Chelsea's Youth Academy. He is the son of ex-professional footballer Andy Kiwomya and the nephew of Chris Kiwomya. He had been a junior athletics champion in the 100m; at the age of 14 he ran the event in 10.98 seconds.
Kiwomya and his girlfriend, Talitha Minnis of Ex on the Beach, have a son named August Alexander who was born on 27 January 2016.
Kiwomya moved from Rotherham United to Chelsea in 2010. Since his move to Chelsea, Kiwomya has featured in the Under-18s, Under-19s and Under-21s squads.
Although Kiwomya did not play a part in the UEFA Youth League final, Kiwomya collected a winner's medal and celebrated with his teammates for his contributions during the group stage.
On 1 July 2016, Kiwomya signed a one-year extension, staying with the London side until June 2017.
He signed a one-month loan deal with Barnsley in January 2015. He was seen as a replacement for Devante Cole, who returned to parent club Manchester City following the expiry of his loan spell. Kiwomya made his senior professional debut with Barnsley, playing 77 minutes in a 2–0 home victory over Yeovil Town. Kiwomya's father Andy had also started career with Barnsley. On 3 February 2015, Barnsley extended Kiwomya's loan deal for a further month, until 3 March 2015. He returned to Chelsea after failing to impress with Barnsley.
On 21 January 2016, Kiwomya joined League One side Fleetwood Town on a one-month loan deal until 20 February 2016. On 23 January 2016, Kiwomya made his debut coming off the bench, replacing David Henen against Doncaster Rovers. On 23 February 2016, Fleetwood decided not to extend his loan and sent him back to his parent-team, Chelsea, after only making four appearances.
On 20 July 2016, Kiwomya joined League Two side Crewe Alexandra on loan until 9 January 2017. On 6 August 2016, Kiwomya made his Crewe debut, coming off the bench in the 62nd minute and scoring the second goal in a 2–1 win at Stevenage. On 16 August, Kiwomya made his first start, against Hartlepool United, setting up the first goal and scoring the second in a 3–3 draw. In September 2016, Kiwomya was nominated for Sky Bet League Two Player of the Month award. Kiwomya suffered a dislocated shoulder in a match against Grimsby Town on 17 September; the injury did not require surgery, with Kiwomya due to return to regular training in October. After returning from injury, Crewe's manager Steve Davis said he had approached Chelsea about extending Kiwomya's loan period beyond January 2017, and the loan was extended to the end of the season on 9 January 2017. On 9 May 2017, Crewe announced that Kiwomya would be returning to his parent club.
After having tried to sign him during the previous season, on 16 June 2017 it was announced that Kiwomya had joined Doncaster Rovers on a three-year deal.
Kiwomya has represented England at under-16, under-17, under-18, and under-19 levels.
Kiwomya has been described by club Chelsea as "a pacey player who mostly operates as a winger but can play as a central striker", and as "an exciting striker with electric pace."As of 17 April 2017.
FA Youth Cup: 2011–12, 2013–14
Professional Development League: 2013–14
UEFA Youth League: 2014–15
Victory Shield : 2012