Giakoumakis, who comes from a Hellenized-Gypsy family, started his career at Atsalenios. In 2012, he signed for Platanias and he debuted for the club in a 3–2 win against Skoda Xanthi, coming in as a substitute in the 78th minute. In January 2014 he signed for Episkopi on loan until the end of the season and he made a total of 11 appearances and scoring two goals. He returned to Platanias, starting playing more often in the 2014–15 season and on 26 April 2015, he scored his first Superleague goal, in a 2–0 home win Panetolikos.
On 23 December 2016, AEK and Platanias have already agreed terms, over the transfer of talented striker to the Greek Cup winners. The 22-year-old player, who is considered to be among the brightest talents at his position in Greece, will join AEK in the summer of 2017 and sign a four-season contract with the team of Spanish manager Manolo Jiménez. On 26 June 2017, Giakoumakis joined AEK Athens from the Superleague Greece on a four-year contract. At his return after an early injury, at Europa match AEK v AC Milan, supporters chanted his name. On 20 December 2017, he scored his first goal with the club in all competitions in a 4–0 away Greek Cup win against Panetolikos. On 4 February he scored as a late substitute, in the extra time with a kick sealing a glorious 2–1 away win game against champions Olympiacos. It was his first goal in Super League with AEK. He scored his first goal for the 2018–19 season, in a 2–1 home win against Lamia for the Greek Cup, taking advantage of Lucas Boyé's excellent solo effort.
On 24 January 2019, after a year-and-a-half in AEK Athens, Giakoumakis signed a six months contract with OFI in the club's effort to avoid relegation, with an undisclosed purchase option for the summer of 2019. On 17 March 2019, he scored his first goal with the club in a crucial 2–0 home win over fellow strugglers Levadiakos to climb above their SuperLeague rivals, however both clubs still sit in the relegation zone. On 3 March 2020, he was loaned out to Ekstraklasa club Górnik Zabrze for the remainder of the current football season. On 30 May 2020, Giakoumakis scored the winning goal for Górnik Zabrze against ŁKS Łódź sealing a vital 1–0 away win for his club. On 23 June 2020, Giakoumakis scored his third goal for Gornik Zabrze in the Ekstraklasa, while teammate Stavros Vasilantonopoulos registered his second marker for the club in the same match. The Greek striker connected with a low pass across the box, neatly turning the ball beyond the goalkeeper into the far right corner, sealing a 3–1 away win game against ŁKS Łódź.
