Vačkář studied composition with Josef Suk (a pupil and son-in-law of Antonín Dvořák), and violin with Karel Hoffman at the Prague Conservatory, and graduated in 1931.
However, the new musical language of pre-war modernism and the spontaneity of jazz prompted him to set out on his own compositional path.
Notable among his chamber music compositions are: Concerto for string quartet, 2 sonatas for violin and piano - Dedication and Musica Intima, Furiant for string trio, the brass quintet, compositions for guitar and flute, guitar and cello, for trumpet and organ, numerous pieces for piano and other.
When he reached the zenith of his creativity, Vačkář became a wholeheartedly modern composer who, nevertheless, remained true to his Czech roots.
In all of his music, harmonies, rhythms and instrumentation are marked by great gusto and dialogue between his inner self and the "roaring world" outside.