A bartender by trade, in 2015, he represented his country with Michal Kočík in the 2015 PDC World Cup of Darts, but they were defeated 5–2 in the first round by the Austrian duo of Mensur Suljović and Rowby-John Rodriguez.

Jirkal became Runner-up after losing to Martin Heneghan from Ireland of the 2018 WDF Europe Cup.

In June he represented Czech republic along with Karel Sedláček in 2019 World Cup of Darts.

The Czech republic team lost in the first round with Poland (Krzysztof Ratajski and Tytus Kanik) 2-5.

[5] It was not really successful journey for him, with just two victories, over Michal Ondo and Daniel Barbořák, he finished 9th after Phase 1 and was eliminated from the tournament.