Paixão's first taste of professional football came in 2009 as he signed for Scottish Premier League club Hamilton Academical on 6 August, alongside twin brotherMarco. He made his league debut nine days later, against Kilmarnock. Paixão was released from his contract with immediate effect on 14 April 2011, alongside his sibling. He appeared in 61 official matches for the Accies, scoring 11 goals.
Tractor
On 2 August 2011, Paixão signed a one-year contract with Tractor S.C. in Iran, for an undisclosed fee. In his first season he netted a club-best ten goals in the Pro League, being voted by Goal.com as best player on the team.
Śląsk Wrocław
Paixão returned to Europe, joining Polish Ekstraklasa's Śląsk Wrocław at the tail end of the 2013–14 campaign. In his first full season he scored 18 goals, bettered only by Kamil Wilczek from Piast Gliwice; this included a hat-trick on 25 October 2014 in a 4–1 win at Lechia Gdańsk.
Lechia Gdańsk
On 8 February 2016, Paixão moved to Lechia Gdańsk for a fee of £100.000 with two years left on his contract, with Śląsk unhappy with the player's behaviour and accusing him of being disloyal– he reunited with his sibling, who arrived earlier from AC Sparta Prague. He scored a combined 26 goals in his first two and a half seasons, adding ten in all competitions in 2017–18, five of which were against Lechia's main rivals Arka Gdynia in the Tricity Derby. The 2018–19 campaign proved to be Paixão's best in terms of goalscoring with 15 goals in total, with him being his team's top scorer and the fifth highest in the league as they finished in third position. He broke a long-standing Lechia record of scoring the most goals for the team in the Polish top division, surpassing previous holder Bogdan Adamczyk on 25 November 2018 after finding the net against Jagiellonia Białystok. He also won the Polish Cup, assisting the only goal of the final on 2 May against Jagiellonia for Artur Sobiech in added time, having earlier had a goal ruled out by the video assistant referee for offside. At the start of the 2019–20, Paixão started in the Polish SuperCup, helping his side win the match 3–1 after defeating Piast. He scored in both legs of the second qualifying round in the UEFA Europa League against Brøndby IF, and as a result became the first club player to achieve the feat more than once in European competition.
International career
During their spell in Poland, both Paixão and his sibling were often poised to be called up to the Portuguese national team, but nothing came of it.
Personal life
Paixão's twin brother Marco was also a footballer, Flávio being the younger by five minutes.
