Kelly Osbourne went after the hairdresser with whom her dad, Ozzy, allegedly had an affair ... with a vengeance.

As you can see, she posted, "Anyone looking for cheap chunky LOW-lights a blow out and a b*** job."

She went on to post her phone number.

Kelly also fired off at someone suggesting Ozzy is at fault too ... saying "my father is almost 70 ever hear of elder abuse?"

Don't mess with the Osbournes.