Sounds like a hoax to me. IANAV, but I’ve never heard of anthrax being transmitted by horseflies or any insect.
Under “How is anthrax transmitted?” on the CDC website is the following:
“Anthrax infection can occur in three forms: cutaneous (skin), inhalation, and gastrointestinal. B. anthracis spores can live in the soil for many years, and humans can become infected with anthrax by handling products from infected animals or by inhaling anthrax spores from contaminated animal products. Anthrax can also be spread by eating undercooked meat from infected animals.”