In 1977, he was awarded a year's scholarship to study composition and arrangement with Herb Pomeroy at Berklee College of Music in Boston.

He then continued his composition studies with Jarmo Sermila, George Crumb, and Václav Kučera.

Since returning to Prague, he has led his own ensembles (primarily quartets and quintets), composed and arranged, and—after the death of Karel Velebný—worked as director of the Summer Jazz Workshops in Frýdlant.

He has made frequent appearances in Finland (with the Finnczech Quartet and in particular with Jarmo Sermila) and Norway (with the Czech-Norwegian Big Band and Harald Gundhus [no]), and has performed in the USA, Japan, Mexico, Israel, Germany, Luxembourg, the Netherlands (at the North Sea Festival), and elsewhere.

As a composer, Viklický has attracted attention abroad primarily for having created a synthesis of the expressive elements of modern jazz with the melodicism and tonalities of Moravian folk song that is distinctly individual in contemporary jazz.