Kossak was born in Drohobych in Galicia (then part of the Austro-Hungarian Empire, now in Ukraine).

He studied law at Lviv University and was one of the organizers of the nationalist movement in Galicia.

He became deputy commander of the Carpathian Sich National Defense Organization in Carpatho-Ukraine.

In 1939, he was taken prisoner and summarily executed by Hungarian troops in Solotvyna, near Bukshtyn, in Transcarpathia.

Also shot was his superior, Mychajło Kołodzinskyj, and a number of other Sich Riflemen.