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:
And for those of you with time to burn, here are 1,600 and some odd websites were it's used without mentioning Bukowski, although many of these could be people borrowing it from Buk: