William Buckley was just 2 years younger than his brother James (N.Y. Senator, 1971-77), who spoke with no noticeable accent. Both were born in New York City.
So what?
Buckley was well known for his command of language. Buckley came late to formal instruction in the English language, not learning it until he was seven years old (his first language was Spanish, learned in Mexico, and his second French, learned in Paris). As a consequence, he spoke English with an idiosyncratic accent: something between an old-fashioned, upper class Mid-Atlantic accent and British Received Pronunciation. Impressionist David Frye included Buckley in his portfolio in the 1960s and 1970s, mastering Buckley's quirky mannerisms, such as his deliberate speech pattern, his use of pen or pencil as a prop, and his tendency to grin and open his eyes wide when making a self-satisfying verbal point.