Kouda was born in
Cantù, Italy to Burkinabé parents. He began his youth career with local club Mariano Calcio, before being admitted to the
Atalanta youth academy after a successful tryout. In 2016, he was released by the club. He then played for the youth teams of
Renate, Luciano Manara,
Caratese and
Cagliari. On 1 December 2019, he made his senior debut with
Caratese in the
Serie D game against
Virtus Bolzano. After three seasons at the club, he scored 8 goals after 44 league appearances. In July 2022, Kouda signed for Serie C side
Picerno, where he netted 2 goals after 32 games in his only season with the club. He scored his first goal for Spezia on 24 November 2023 against
Sampdoria. On 30 August 2024, Kouda signed a contract with
Parma and was loaned back to Spezia for the rest of the 2024–25 season. On 12 August 2025, he returned to Spezia on loan for the 2025–26 season. On 23 January 2026, Kouda moved on a new loan to
Mantova in
Serie B. ==International career==