Don’t know about ritzy east coast private schools in the 80s, but in Ohio rust belt high schools of the 70s “boof” was a contraction. Referring to a particular unsavory sexual practice. Haven’t heard, thankfully, that term for decades. Never knew it had any other meaning.
Short for "butt-f*****".
I'm from Ohio myself, but NEVER heard the word "boof".
In any context.
It probably does mean fart in Kavanaugh's case.
It certainly isn't a common term.
Maybe some made up word that only he and his friends knew the meaning of.