The 31-year-old TV presenter was spotted enjoying a meal with the 17-year-old singer earlier this week, fuelling speculation that the two are dating.
Furious fans of the heartthrob took to Twitter to vent their anger at Flack for seeing a lad 15 years her junior.
One tweeter posted that Flack “should be having kids, not dating them” and branded her a “saggy old woman”.
Another die-hard fan wrote: “If Caroline Flack flirts with my boyfriend I will personally hunt her down and shoot her,” while yet another posted: “I want to kill you Caroline Flack, Harry is mine B***h.”
Styles telephoned Flack to comfort her in the wake of the threats, according to a source.
Flack has already posted her own response to the threats on the social networking site, writing: “Hi one direction fans! To clarify. I’m close friends with harry. He’s one of the nicest people I know… I don’t deserve death threats. 🙂 x.”