From 1975 to 1979, he studied classical guitar as a teenager at the Prague Conservatory[1] and learned jazz through his mentor, Karel Velebný.

The following year he moved to New York City, where he studied at the New School for Jazz and Contemporary Music with John Abercrombie, Dave Liebman, and Arnie Lawrence.

He studied privately with guitarists Jim Hall and John Scofield and before leading his own group.

[1][3] Linka has performed and recorded with Jon Batiste, Larry Grenadier, Gil Goldstein, Paul Motian, Bob Mintzer, John Scofield, John Abercrombie, Kenny Wollesen, and Marvin "Smitty" Smith on labels such as Timeless, Enja, Sony BMG, and Universal.

Linka is the founder and artistic director of the Bohemia Jazz Fest which takes place every July in the Czech Republic.