Flores made his official league debut in the Torneo Descentralizado on 31 July 2011 in an away match against Juan Aurich for round 16 of the 2011 season, at the age of 17. He entered the match in the 64th minute for Andy Polo, and the final result was 1–0 in favor of the Chiclayo based club. Later in match day 23 he played in his first Peruvian Clásico in the Descentralizado on 24 September 2011 at home in the Monumental. At the time of the derby Alianza Lima was in first place in the league. He entered the match in the 68th minute for Miguel Angel Torres when the score was tied at 1–1. Then late in 92nd minute of the derby, Flores managed to dribble past three Alianza Lima players and provide the pass that led to Martin Morel’s winning goal. The derby finished in a 2–1 win for Universitario.

On 31 August 2012, Flores was announced as the new signing for Villarreal’s reserve team, Villarreal B.

He had played for all youth level of Peru, and was part of U-20 squad in the 2013 South American Youth Football Championship, where he left a great mark in his career. In the final match against U-20 Chile, which Peru had to win and eliminate Chile to qualify for 2013 FIFA U-20 World Cup, he scored from a header to put Peru a lead. However, his side could not protect this advantage because of a superb free kick from Bryan Rabello which levelled the game. It eventually ended 1–1 and Chile qualified at the expense of Peru, but Flores’ performance impressed then-manager Sergio Markarián and he was called to the senior squad for the first time in perpetration for the friendly against South Korea and the remaining matches of 2014 World Cup qualifying, but he only made his debut in the friendly against South Korea. Peru’s failures to qualify for both U-20 and senior World Cup had been a dark mark on his career and he became less used.

On 11 August 2016, Flores move to Danish-side AaB was confirmed. After interest from Belgian, Dutch and Spanish sides, Flores signed a 4-year deal. On 28 August 2016, he scored his first goal in the Danish Superliga, as he provided the equalizing goal in a 2–1-win against Aarhus Gymnastikforening.

In May 2018, he was named in Peru’s provisional 23 man squad for the 2018 World Cup in Russia.

On 14 January 2020, D.C. United acquired Flores and paid a $5 million transfer fee. His move to D.C. United was the club-record transfer fee. Flores made his debut on 29 February 2020, in a 1–2 loss against the Colorado Rapids. In late August, Flores suffered a head-on-head collision and will be out 4–6 weeks to repair facial fractures. He returned from his injury on 11 October 2020, in a 1–2 loss against the Chicago Fire. On 1 November 2020, Flores contributed his first assists for the team, providing two in a 3–4 loss against the New England Revolution.