Kieffer was on trial with Exeter City in December 2015 whilst at Viking in Norway. He also had a trial with Leyton Orient before signing for Forest Green Rovers.

Kieffer attended secondary school in Totnes and, with the demise of Torquay United's youth scheme, found himself playing for Paignton Saints in the South Devon League. His big break was to join Truro City in 2012 moving on to Dorchester Town early in 2013. After a brief - but successful - spell in Dorset, he signed for Yeovil Town in time for the 2013/14 season. After making fifty first-team appearances in the Championship and League One, Kieffer was released at the end of 2014/15 as the Somerset club faced up to a second relegation. 

It was at this point that he played a summer and autumn in Norway before arriving at Exeter City for a trial once the season was over and he was back home in Devon.

After Norway, Kieffer's time at Forest Green Rovers was punctuated by a short loan at Torquay United, his hometown club. In one of his few games at Plainmoor, Kieffer scored a hat trick against Solihull Moors. Returning to and later leaving Forest Green, Kieffer's career took an upward turn as he played for Ipswich Town, Barnsley, Wigan Athletic and Cardiff City.                

After particular success at Cardiff, Kieffer transferred to AFC Bournemouth for an undisclosed fee in January 2022. At Dean Court he quickly sustained an injury but returned in April for Bournemouth’s promotion run-in. He was to score the match-winner against Nottingham Forest which secured Bournemouth's promotion to the Premier League. With another goal the following week, Kieffer had scored four goals after just eighty-three minutes on the pitch since joining the Cherries.

Kieffer scored on his Premier League debut against Aston Villa in August 2022 and, after netting ten goals in 46 league and cup games, rejoined ipswich Town on loan at the start of February 2024. Starting fourteen times - with another four appearances from the bench - he scored seven times during the rest of the season as he won promotion from the Championship for the second time in his career. Returning to Bournemouth at the end of the season, he subsequently moved to Sheffield United in July 2024.

Having made his debut for Wales in 2019, Kieffer was to play a part in all three of Wales’ games in the 2022 World Cup in Qatar; starting two games and coming on as a substitute in the other. By the time of his 2024 move to Sheffield United, Kieffer had played 43 times for Wales scoring twelve goals.