Someone from Louisiana had a receipe for a permethrin based fly spray that actually worked.  I'm in Florida, if it works in LA it will work in FL.

This doesn't answer your question, but I'm sharing in case you find it helpful. I'm in South Georgia, much like the climate and bug situation in LA and FL....Smartpak's OutSmart Fly Spray is absolutely incredible! It works on everything from gnats to mosquitos to flies, etc. I even put a dab near my ears to keep the gnats and flies away from me.

If you haven't tried it, I really recommend it.

I found last year that peppermint oil mixed with water and a few drops of dawn works great. It's basically what SmartPaks fly spray is. And $10 worth of peppermint oil makes me enough for a whole season. I had to adjust the strength a few days to find the right mix, but works better for me than the store bought sprays 

Do you know what your approximate ratio of oil to water was? 

I've kind of adjusted it as needed, some months are heavier for bugs than others. But I fill an old ultrashield bottle with the water, just 3-4 drops of dawn is fine. I shake that a little bit and then add around 20 drops of the peppermint oil. It's not always super easy to count when you're tapping it into the bottle. I just get the oil at walmart by the diffusers. I can't smell, so I can't fully judge how strong it is. I've done extra drops when its god awful hot sticky muggy and they're just being swarmed. It was 94 here yesterday and muggy and i sprayed a little on my hand and wiped the sides of my head and I wasn't bother by the gnats or flies 

I have been feeding Solitude with success.  It really has kept the fly population down - its about a hundred a bucket but it lasts a long time.

We had a mild winter in Oklahoma so the flies will be insane here.

Thank you for sharing!

What's the purpose of the Dawn in the mixture?

It seems like it just helps the oil mix a little better with the water, and it's also fairly unpleasant for bugs as well. I really liked the SmartPak OutSmart, which also has soap in it. So I basically just tried to recreate it in a more affordable way. I had put the rubbing alcohol in too, but didn't think it made a difference and its drying effect wouldn't be great for my black horse in the sun. But I found the water, dawn, and peppermint oil works the same. And is like $0.50 a bottle in the end. And you don't have to use dawn, any soap would probably work. Another that works decently well is dawn, water, vinegar, and listerine all mixed together. Squirt of dawn, 1/2 cup vinegar, 1 cup listerine, & the rest of the bottle water 

The recipe I got from Tyrney stienhoff  is 2 oz skin so soft, 2 oz permethrin & 32oz  water. I double the recipe cause I have 5 horses. Works great & my horses smell good to  :)  And if I get any in my face, I don't cough my lungs out. 

This is what I use. Go to Walmart and get a 1 gallon sprayer. They were about $6. Now probably about $10. Mix as directed. This works better than anything I have found and is most economical. Really keeps the flies off. If you have a mosquito problem, a couple of glunks  of AVON SKIN SO SOFT helps a much. I have used this for years and it has probably saved me about $300 a year. I have a lot of insects. This even gets those big black flies. I live in NE TX, just west if Shreveport. Guess I need to post the product!!!

https://www.valleyvet.com/ct_detail.html?pgguid=C889A73D-888F-49AE-B3B8-A578CEC2D640

The Dawn acts as a surfactant.