Kennedy attracted the attention of Stevenage in the summer of 2013, having been scouted by then-Stevenage Academy Manager Darren Sarll whilst playing for Northern Ireland at youth level. Sarll spoke to Kennedy's parents and offered Kennedy the opportunity to train with the club's youth academy. He accepted the offer, played one match for the Stevenage U18 team and subsequently signed a two-year scholarship with the club ahead of the 2013–14 season. The following season, Kennedy impressed Stevenage manager Graham Westley whilst competing in the 2014–15 FA Youth Cup, particularly in the club's 2–1 extra-time defeat to Everton in the Third Round of the competition in December 2014. Two days after the match against Everton, he was offered the chance to train with the first team, and he made his first-team debut a month later, on 31 January 2015, coming on as a second-half substitute in a 2–0 League Two defeat against Oxford United at Broadhall Way. A week later, he made his first starting appearance, playing the whole game in a 1–0 loss away to Mansfield Town. Kennedy scored his first professional goals the following week, on 14 February, netting twice as Stevenage secured a 3–1 victory away at Hartlepool United. Four days after scoring his first two goals for the club, he signed his first professional contract. Kennedy scored four goals in 17 games during his first season in professional football, helping Stevenage reach the League Two play-offs, where they lost at the semi-final stage to Southend United. Kennedy had to wait until late September to make his first appearance of the 2015–16 season as a result of undergoing hip surgery in the summer of 2015. He was a regular feature under new Stevenage manager Teddy Sheringham upon his return from injury, helped by scoring two goals within the space of four days shortly after his return. Four days after his goal against Exeter, on 15 October 2015, he signed an improved three-year contract with the club. Kennedy was given personal leave "for a few weeks" in December 2015, before sustaining a knee injury in training a month later that was reported to likely keep him out of action for the remainder of the season. However, six weeks after knee surgery, Kennedy came on as a 71st-minute substitute in a 2–0 home loss to Exeter City. Sheringham was replaced as manager by Darren Sarll, who bought Kennedy to the club three years earlier. He made 25 appearances in an injury-hit season that marked Kennedy's first full season as a professional, scoring three goals, as Stevenage lost just once in their remaining nine league fixtures to secure their League Two status for a further season.
2016–present
Following an injury-free pre-season, Kennedy began the 2016–17 season as a regular starter. He opened his scoring account for the campaign when he tapped in Charlie Lee's deflected shot to score the only goal of the game in Stevenage's 1–0 victory over Ipswich Town at Portman Road in the EFL Cup. Kennedy scored from 30-yards in the club's first away win of the season in October 2016, with his left-footed curling effort dipping under the crossbar and into the back of the net, as Stevenage secured a 2–0 win at Morecambe. He scored his final goal of the campaign in a 2–0 away win over rivals Luton Town. The goal was voted as Stevenage's goal of the season as Kennedy chested the ball down just inside Luton's half, dribbled to the edge of the area and unleashed a right-footed shot into the top corner of the net. In April 2017, Kennedy signed a new two-year contract with Stevenage, running until the summer of 2019. Kennedy scored nine times in 39 appearances during the season as the club finished in tenth place in League Two. Kennedy joined fellow League Two club Newport County on loan on 31 January 2019 for the remainder of the 2018–19 season. Stevenage chairman Phil Wallace stated the club had "little choice" in the loan move with Kennedy having "made it clear" that he did not want to remain at the club, feeling that "a different environment would allow him to play his best football". Kennedy made his Newport debut in the club's 3–0 away defeat at Grimsby Town on 2 February 2019. He made ten appearances during the loan spell, scoring once; his goal for the club came in a 3–1 victory at Yeovil Town on 30 March 2019. Kennedy was released by Stevenage at the end of the 2019/2020 season.
International career
Having earned two caps for Northern Ireland's U17 team in 2013, Kennedy made the step up to U19 level following his breakthrough into the Stevenage first team in 2015. He captained the under-19 team and scored two goals in five appearances. Kennedy was called up to the U21 team in October 2016, and played seven times at that level.
