Kokosha qualified for the men's 4 × 200 m freestyle relay, as a member of the Ukrainian team, at the 2004 Summer Olympics in Athens. Teaming with Serhiy Fesenko, Serhiy Advena, and Dmytro Vereitinov in heat one, Kokosha swam a second leg and recorded a split of 1:52.03, but the Ukrainians settled for sixth place and twelfth overall, in a final time of 7:24.13.