Transcripts and audio clips of Kissinger’s telephone conversations are now available as part of the Digital National Security Archive (via OxLIP+). To search or browse this collection alone, tick the relevant box on the ‘documents’ page (link on the left hand side). If you scroll down this screen there is also an option to restrict your search/browse to audio clips only.
Related to this, the Miller Centre of Public Affairs makes freely available a selection of more transcripts and recordings of telephone calls and speeches for Roosevelt, Truman, Eisenhower, Kennedy, Johnson and Nixon. See http://tapes.millercenter.virginia.edu.