I like the term Poet Laureate of Skid Row. Though no, I don't think Buk is "beat". There's a quote on the back of the "new" print of Post Office... something about the Beats taking poetry far, and Buk took it further.
I don't know where the term came from, I just always see it everywhere Buk is mentioned.
"Poet Laureate of Skid Row" sounds like it may predate Bukowski's rise to fame. It could be a term that has been around a long time and was merely adapted for Bukowski. Going to Google, it was used -- for example -- to describe Nelson Algren: