Zinchenko has competed in major tournaments, including the 37th Chess Olympiad in Italy in 2006, where he won an individual silver medal while playing for Ukraine. He also competed in the Ukrainian Chess Championship in 2005, ending in sixth place.

In team play, he has represented Ukraine in the –21 championship in 2002, finishing in the top three. Additionally, he played on Board 5 for Ukraine in the World Team Chess Championship in Beersheba, Israel in 2005, helping Ukraine to a second-place finish. One of his significant victories was in 2007 when he beat the previous World Chess Champion Karjakin at the Torshavn International.

Zinchenko also coaches chess, and has worked with international champions such as Women's World Chess Champion Maria Muzychuk. As an evidence of his influence in the field, the Slav Defence in chess now includes the "Zinchenko Variation," named after him.