BFBS was generally brought out when a team either added a black jersey when one didn't previously exist, or introduced black to its color scheme just to sell more merchandise (because black merchandise sells). A team doesn't necessarily have to have worn a black jersey to be BFBS, but it's a big indicator.
Starting with the Gretzky-era Kings, I think the leagues saw huge potential marketing opportunities with entertainers who wore black on stage and in videos, especially rap acts from California.
For MLB, I would include the Royals, Mets, Rangers, A's, and Marlins. The original Marlins were Teal, sliver, and black, but before moving to the dome, they emphasized black and silver over anything else. I find it hard to include the Reds. Most people seem to associate the Reds with the Big Red Machine era, but between the 50's and 60's, they sort of bounced between navy and black for contrast with the red. I believe the vests with names under numbers era was red and black. You could also say the movement started with the White Sox, who seemed to change uniforms and logos every season in the 70s and 80s. But in all those looks, they wore various shades of red and blue. Then they moved to a much more drastic change of black and silver, worn to this day.
For the NBA, up until the expansion era there weren't many teams wearing black through the late 80s except for San Antonio and Sacramento. But Miami and Orlando came in with black jerseys, then league-wide more teams started wearing alternate jerseys that include a black set. Chicago is one, for example. Vancouver had a black set. Phoenix did as well. Philadelphia and Washington both revamped their schemes, with Philly more of a BFBS (red, white. blue, and black). Washington changed their uniforms (and name) to match their arena cohabitants, the Capitals, with both teams going blue, black and bronze (a dual BFBS). By the mid 2000's, the majority of teams had either a black alternate jersey, or added black to its scheme.
The NFL has a bit more control over its teams' color schemes and looks. The only teams I can think of that added black jerseys where none previously existed were Arizona, Philadelphia and Jacksonville, but all three did have black already in their palettes,. I think Baltimore had a black jersey earlier in the franchise's existence.
For the NHL, I'd say Buffalo and Washington were BFBS when they had major redesigns. Possibly Anaheim as well, when they moved away from the DIsney-era look. Carolina's look made sense - hurricane flags are red and black. But the black alternates were more recent.
There may be teams I'm missing. And I won't get into the NCAA - too many teams and sports to cover those that added black for no reason.