Flores came through the youth system at Universitario de Deportes in the Peruvian first tier. Playing at the U-20 level, the midfielder represented his club at the 2011 U-20 Copa Libertadores. Flores led Universitario to a championship victory over Argentinian side Boca Juniors and was named the tournaments best player. The midfielder then went on to make his debut for the senior squad as a substitute during a 2-0 victory over Colegio Nacional Iquitos on Aug. 7, 2011. The Peruvian spent his first two professional seasons with his boyhood club before being shipped out on loan for the 2013/14 season to Valencia CF B in the Spanish third division.
During his time with the Spanish side, Flores recorded four goals across 29 appearances. Following his loan spell, Flores returned to Peru and went on to become a regular for Universitario making 99 appearances, recording 15 goals and 27 assists. In 2016, the Peruvian returned to Europe to join Aalborg BK in the Danish first division. During his second stint in Europe, Flores flourished for the Danish side as he made 52 appearances recording four goals and six assists.
After two seasons with Aalborg BK Flores transferred to Club Atlético Monarcas Morelia in Liga MX. With the Mexican club, the 25-year-old excelled as he recorded 12 goals and six assists in 47 appearances. Following an impressive two seasons in Liga MX, Flores was acquired by D.C. United for a club record fee.
Flores represented Peru at the U-17 and U-20 levels before making his debut for the senior squad during an international friendly with South Korea on Aug. 14, 2013. Flores went on to become a regular for the Peruvian national team as he has now made 47 appearances in all competitions and recorded 13 goals in the process. Prior to the 2018 FIFA World Cup, Peru had failed to qualify for the tournament since 1982. Flores was a major component to the Peruvians success leading up to the 2018 FIFA World Cup. In the qualification matches, Flores made 14 appearances recording five goals and an assist. While at the World Cup, Flores started all three matches for Peru, though they were unable to advance past the group stages.
During the 2019 Copa America, Flores played in all six matches and helped Peru reach the final of the tournament. In the group stages, the 25-year-old recorded one goal during the 3-1 victory over Bolivia. After helping his country advance to the knockout stages, Flores scored the game-winning penalty for Peru as they defeated Uruguay in a shootout to advance to the semi-finals. In the semi-finals, Peru went up against their rivals Chile. Flores continued his scoring form with another goal to help Peru cruise to a 3-0 victory, though Peru were ultimately defeated in the finals by Brazil. The midfielder has made ten total appearances in the Copa America for Peru recording three goals and an assist.
January 13, 2020: acquired on permanent transfer from Liga MX (Mexico) side Club Atlético Monarcas Morelia.