The "greatest generation" doesn't really match up with any single generation, it is really a vague and undefined creation of the left that they find useful, Silver Star awarded Lyndon Johnson was a sailor during WWII as were the other Vietnam Presidents, Kennedy and Nixon and Ford, all Navy WWII vets.
Here is a list of the leaders of the Vietnam War, Presidents and civilians (political), and the military, ALL OF THEM were WWII vets except for Schlesinger.
United States of America Political:
Dwight D. Eisenhower was the 34th President of the United States from 1953 to 1961.
John F. Kennedy was the 35th President of the United States from 1961 until his death in 1963.
Lyndon B. Johnson was the 36th President of the United States from 1963 to 1969.
Richard Nixon was the 37th President of the United States from 1969 until he resigned in 1974.
Gerald Ford was the 38th President of the United States from 1974 to 1977.
Robert McNamara was the 8th Secretary of Defense, serving under Presidents John F. Kennedy and Lyndon B. Johnson from 1961 to 1968.
Clark Clifford was the 9th Secretary of Defense, serving under President Lyndon B. Johnson from 1968 to 1969.
Melvin R. Laird was the 10th Secretary of Defense, serving under President Richard Nixon from 1969 to 1973.
James R. Schlesinger was the 12th Secretary of Defense, serving under President Richard Nixon and Gerald Ford from 1973 to 1975.
Henry Kissinger was the 8th National Security Advisor and the 56th Secretary of State, serving under Presidents Richard Nixon and Gerald Ford from 1969 to 1977.
Military:
Earle Wheeler was a United States Army General who served as Chairman of the Joint Chiefs of Staff from 1964 to 1970.
Thomas Hinman Moorer was a U.S. admiral who served as Chairman of the Joint Chiefs of Staff from 1970 to 1974.
William Westmoreland was an American General who commanded American military operations in the Vietnam War from 1964 to 1968.
Creighton Abrams was an American General who commanded American military operations in the Vietnam War from 1968 to 1972.
Frederick C. Weyand was a U.S. Army General who was the last commander of American military operations in the Vietnam War from 1972 to 1973.
Elmo Zumwalt was an American naval officer and commander of American naval forces in Vietnam.
William W. Momyer was commander of the U.S. Air Force Tactical Air Command and the commander of the 7th Air Force.
John S. McCain, Jr. was an American admiral and Commander-in-Chief of the Pacific Command.
Eisenhower was not a president during the Vietnam war, which JFK started, President Eisenhower merely had advisers there just like we do in many dangerous places without engaging in a war.