Slavia Prague Kuchta made his
Czech First League debut for
Slavia Prague on 8 November 2015 in a game against
Bohemians. In January 2019, he joined
Teplice on loan until June 2020. In February 2020, Kuchta signed for
Slovan Liberec on a permanent deal, following a loan move at the club. In July 2020, Kuchta re-signed for Slavia Prague. Kuchta finished the
2020–21 Czech First League as joint top scorer, alongside
Adam Hložek with 15 goals. In the final match of the season on 29 May 2021, Kuchta scored his side's winning goal against
Dynamo České Budějovice which confirmed an undefeated league season for Slavia, the first time a Czech club reached this milestone since rivals
Sparta Prague did so in
2009–10. He made his league debut for Lokomotiv on 6 March 2022 against
FC Khimki and scored the winning goal in a 3–2 victory. However, he never served a disqualification that he received for getting sent off in his last game for Slavia, and, according to FIFA regulations, was not eligible to play, FC Khimki filed a protest. The protest was denied on 10 March 2022, according to
Russian Football Union, Kuchta should have been disqualified for the
Russian Cup game Lokomotiv played against
Yenisey Krasnoyarsk on 3 March and lost 4–0, as Czech regulations extend disqualifications to Cup games, even though Russian regulations do not, so he was technically disqualified for "one league or Cup game" as opposed to "one league game". Lokomotiv did not provide the document detailing the disqualification to the league, the club claimed they did not receive it during the transfer, and he was allowed by the RFU to play in the Cup game. His disqualification is considered served after that game, even though he actually played in it, as per FIFA regulations. Khimki considered lodging an appeal.
Sparta Prague In June 2022, Kuchta joined
Sparta Prague on a one-year long loan with an option for a permanent transfer. In his first match for Sparta Prague in the Czech First League (2–1 home loss against
Slovan Liberec) he stepped on Liberec goalkeeper
Olivier Vliegen's head and received a yellow card, which the referee changed to a red card after he saw video footage. Kuchta was banned for five league matches by LFA Disciplinary Commission. The club with Kuchta appealed his ban, but the appeal was rejected by Appeals Committee on 11 August 2022. Kuchta helped the club to win its first championship title since 2014. In June 2023, Sparta exercised the option to buy in the loan contract, signing a multi-year contract with Kuchta. In May 2024, Kuchta helped the club to win its second championship title in two seasons and domestic cup. He was awarded as the forward of the
2023–24 season by the League Football Association.
Midtjylland On 31 August 2024, Kuchta signed a contract with
Danish Superliga club
Midtjylland until 2028.
Sparta Prague (loan) On 15 January 2025, Kuchta joined Sparta Prague on half-year loan deal with option for a permanent transfer.
Sparta Prague On 30 May 2025, Kuchta signed a multi-year contract with Sparta Prague. ==International career==