After graduation, Walker joined the United States Military Academy Band at West Point; at the same time, he studied flute with Harold Bennett, principal flutist of the Metropolitan Opera Orchestra.
Other significant teachers have been Sarah Fouse, Francis Fuge, James Pellerite, and Claude Monteux.
After eight years in Pittsburgh, he was appointed by Zubin Mehta as principal flutist with the Los Angeles Philharmonic, a position he held from 1977 until 1984.
He also played principal flute for the New York Philharmonic (under Mehta) for that orchestra's 1982 South American tour.
He has conducted flute master classes and clinics in the U.S., Canada, Europe, South America, Korea, Japan and Russia.
He joined classical guitarist Scott Tennant on his 1998 album Wild Mountain Thyme (Celtic Music for Guitar), performing Ian Krouse's "Da Chara (Two Friends)”.
He is one of four performing artists (with Wynton Marsalis, James Galway and Eddie Daniels) to be named as members of the Board of Advisors for "Smartmusic", a computer program which provides music accompaniments.