Healey started his career with Connah's Quay Nomads, joining their youth setup at Under-16 level in 2009. He made his first team debut for the club as a substitute during a 6–1 victory on the opening Cymru Alliance match of the 2011–12 season against Caersws and made 10 league appearances as the club won promotion to the Welsh Premier League. The following season, he made his debut in the Welsh Premier League, coming off the bench against Bangor City and went on to score 12 league goals for the club during the first half of the 2012–13 season. His prolific form saw him attract the attention of several clubs and Healey spent time on trial with Stoke City and Manchester City.
On 28 January 2013, he signed for Cardiff City. In March 2014 he signed a new contract with the club. On 11 May 2014, he made his first-team debut, on the last day of the season, in a 2–1 defeat against Chelsea as a substitute in place of Craig Bellamy. Healey signed on loan for League One club Colchester United on 19 September 2014. He joined the club as back-up to first choice striker Freddie Sears, initially signing until 20 December. Healey made his debut, coming on as a substitute in the second half, and scored in a 3–0 win over Crewe, which was followed with another in the next game, in a 4–2 loss against Preston North End. Having made ten appearance and scored four times so far, Healey loan spell with Colchester United was extended further until the end of the season. On 19 March 2015, Healey was recalled by his parent club Cardiff. On 2 April 2015, in a bizarre turn of events, Healey was re-loaned to Colchester United as a protracted loan move to League 2 team Newport County fell through after the move was blocked by FIFA. A decision that was branded unbelievable by Newport manager Jimmy Dack. On 1 September 2015, Healey signed for Scottish Premiership club Dundee on loan until January 2016. He made a total of 7 appearances for the club, scoring once during a 2–1 defeat to Kilmarnock, before his loan spell was ended early following an injury. On 31 August 2016, Healey joined Newport County on loan until 3 January 2017. He made his debut for Newport on 10 September 2016 in League Two during a 2–2 draw with Cheltenham Town as a second-half substitute in place of Jon Parkin. He scored his first goal for Newport on 24 September 2016 in a 2–1 defeat to Cambridge United. He returned to Cardiff at the end of his loan spell, making his final appearance for Newport in a 2–1 defeat to Wycombe Wanderers on 2 January. Upon on returning, Healey found himself placed on the bench for Cardiff City for the first time in 3 years against Aston Villa. On 21 January, he scored the winner against Burton Albion, also his first for the Bluebirds, after replacing Junior Hoilett. During his second start for the club against Rotherham United on 18 February, Healey was forced off after suffering a serious knee injury, which ruled him out for up to nine months. During his recovery from the injury, Healey signed a new two and a half year deal at Cardiff, before making his first team return on 26 December 2017, coming on for Loïc Damour against Fulham. He joined Torquay United on loan in March 2018 for the remainder of the 2017–18 season, scoring six times in eight appearances including a hat-trick during a 4–3 defeat to Guiseley. On 24 August 2018, Healey joined League Two club Milton Keynes Dons on loan until January 2019. He scored his first goal for MK Dons in an EFL Trophy tie against Peterborough United on 4 September 2018.
Milton Keynes Dons
On 16 July 2019, Healey returned to former loan club Milton Keynes Dons on a permanent basis, signing for an undisclosed fee. In his first game back at the club, Healey scored a 93rd-minute winner in a 1–0 home victory over Shrewsbury Town.
