Vokáč earned his International Master title in 1985 and his Grandmaster title in 1992. He has won a total of three Czech National Championships; the first in 1993, the second in 2005, and the third in 2009. He was a member of the Czech national chess team that won a European Team Chess Championship in 2005.
In 1988, Vokáč won a memorial tournament in favour of Luděk Pachman, a prominent Czechoslovak-German grandmaster. In 2005, he became the first ever Czech champion to win a tournament open to all nationalities in Mariánské Lázně.
In addition to playing, Vokáč has also held administrative roles within the chess community. From 2001 to 2005, he was a member of the Central Committee of the Czech Chess Federation.
Vokáč is also known for his scientific career as an employee of the Czech Technical University in Prague, where he works in the Software Engineering department. He completed his Ph.D. in artificial intelligence in 1997.