Although I can't find all the exact dates (try searching on "KNOB" in the archives ... you'll get a few hundred hits), I am relatively certain that the move to Baldwin Hills was around the same time as KJLH and KSRF moving there.
KJLH had moved on a STA that was granted May 12, 1976 (after then-owner John Lamar Hill's original application to move there from Dominguez Hills was denied four years earlier) , and applied for those facilities to be made permanent shortly thereafter; the STA request had only been approved originally because his landlord at the other site was evicting him, according to a note in Broadcasting about it and the application was denied and appealed multiple times before being approved October 17, 1984. By that time, of course, KJLH had been sold to Stevie Wonder's Taxi Productions.
KSRF, which had been atop the office building at Ocean Ave./Wilshire Blvd. since 1971, had filed originally to move in 1979, but that took until August 31, 1983 to be approved; co-channel KOCM Newport Beach held it up by requesting a hearing on whether their grandfathered short-spaced signal would receive interference from the new facilities, even though KSRF also proposed a substantial decrease in ERP.
I'm guessing, then, that KNOB moved right before they were sold to Spanish Broadcasting System (becoming KSKQ) in 1986, based on the new ERP not appearing in the Broadcasting Yearbook until after the sale. It changed calls again, to the present KLAX, in 1992. The filing to move to Flint and change COL was in 1996, and was originally denied before being granted on appeal two years later.
(It doesn't take much to spark me into researching stuff like this ...)