That's a good question, and I think the exact transmission risk of diseases by BSF depends especially on the insect's diet.
As far as I know, Black soldier fly larvae have not transmitted diseases to humans so far. One of the differences with houseflies is that adults do not feed on larval food sources, which reduces the risk of disease transmission in the wild. However, BSF larvae can contain food-borne pathogens depending on the type of diet they are fed (see Wynants et al. 2018 Article Assessing the Microbiota of Black Soldier Fly Larvae (Hermet...
) and decontamination of the insects prior to use as feed/food is important.
Also, regarding COVID-19, edible insects are unlikely to play a role in virus transmission, see the recent publication by Marcel Dicke et al. 2020 (Article Edible insects unlikely to contribute to transmission of cor...
).
Hope this helps. I'd be happy to hear other thoughts on this topic.
"Although they are not known as a disease vector, adult soldier flies are a potential mechanical vector of various pathogens. A more likely negative interaction would be accidental ingestion of black soldier fly larvae by animals or humans"