It's extremely helpful that you included the actual ingredient list in your question, rather than a brandname - thank you!
So you know, I grow anything that I eat organically and this question is one of the reasons why I do (the other reason is that I was once a Certified Pesticide Applicator for five years, and the training you receive to get that certification makes you never want to use pesticides again, especially insecticides and fungicides).
Now that you know my bias, I can tell you that I would NOT use this insecticide:
- Allethrin is considered mildly toxic if ingested. Here's an impartial analysis. Ingesting it will not kill you, and I doubt that the amount in the insecticide will do much harm - especially if you ingest it only infrequently, but interestingly, if you have hay fever then you're more at risk. It is highly toxic to aquatic life, however.
- Permethrin is an insecticide and an acaricide (tick and mite killer). It is about as toxic to humans as allethrin, but is very toxic to cats because their bodies cannot quickly break down the chemical. In fact, permethrin is popular as a spray for trousers and shirts to prevent tick bites, but cats can ingest it if they sit on the lap of a human who's wearing permethrin-treated trousers (they injest it while grooming). Here's an impartial analysis. Note that in the link it says "The U.S. EPA decided that permethrin was "likely to be carcinogenic to humans" if it was eaten." No indications as to how much must be eaten to get cancer, though - I would assume that it would be a much larger amount than in this insecticide.
- Piperonyl butoxide is a chemical added to pesticides in order to enhance the toxicity of other chemicals in the mix. It is considered to be safe for application to food before harvest, but can cause digestive issues if consumed in large quantities (so, it should be safe in the percentage used in the insecticide that you're inquiring about). More info is here.
An extremely important note when researching any pesticide is to pay attention to the date of the research. Much of the information available is from the 1990s, and much has improved in the way in which chemical studies are done since then, so newer research should be better (but also can be influenced by the politics of the people doing the studies, unfortunately). Also, pay attention to phrases like "not known", "not available", and "not determined" when used with "toxicity", "exposure", and especially "carcinogenic", "mutagenic", or "teratogenic". These phrases indicate holes in the research that could injure or kill you.
Also, pesticide Safety Data Sheets were prepared by the manufacturer for submission to the US government, so, given that many pesticides have been voluntarily removed when their initial permissions came up for renewal, I'd take the information in the SDSs with a grain of salt.
A bigger question is "WHY?", as in "Why do you think you need to spray your herbs with a potential poison?" You have flies - what kind? If they are whiteflies, have you tried sticky traps? Are the plants indoors? If so and it's in a greenhouse, have you tried sticky traps and targeted beneficial predators? There are many, many options to spraying your food with something that could in time harm you or your relatives.
I very strongly recommend that you look into Integrated Pest Management. This is a program meant to minimize the use of pesticides while protecting your crops or other plants. The link I've included contains this link that you can use to further research any chemicals you want to add to your garden.