I have searched for it, but everything what I found is that A0620-00 (the current closest black-hole to Earth) is a slow spinner with Kerr factor $a=0.12$.
How about the Kerr factor for Sagittarius A*?
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With current technologies the Kerr parameter could not be precisely estimated yet.
The best result today is a Kerr factor $a=0.52$.
Better estimates are expected within the next two decades, according to the article.