What exactly the 'Deep Litter Method' is depends on who you ask. My understanding of the term is that it's a naturally composting, healthy soil that doesn't need cleaning out, ever.
Some people think they're doing it on concrete, while cleaning it out every few months; but functional deep litter, of the composting sort that controls problem fungi, bacteria etc, cannot work on concrete as it doesn't drain and therefore creates a stagnant, anaerobic environment that the harmful microbes etc thrive in.
I've not used pine shavings for deep litter, only hay, dirt, etc; most deep litter method users I see who are using pine shavings haven't actually got a composting litter going, they're just building up litter; the term 'deep litter method' is used for both non composting, and composting litters but there needs to be some distinction made. Many people use the non composting deep litter method and expect the results of the composting deep litter method, which of course cannot happen.
The flies may be there for a few reasons. There's a good chance it's to breed; poop that's not broken down properly is often high in protein and their maggots can live in it and feed off it. If that's what they're doing there's a good chance your lower levels of litter have maggots in them.
You may have just hatched a large batch which are now attempting to repeat the cycle. There should be no smell that attracts them though, so I assume your deep litter isn't quite functional yet. There may be a food source in the coop that is attracting them besides the poop.
Depending on what your coop floor is made of, you may not be able to do the deep litter method where you are, at least, not the composting sort. Using lime (pure calcium carbonate, not any of the caustic ones, only the sort that can also be added to their food) will control odor and deter flies as well as destroying pathogens, parasite eggs, etc, but permanent control of these things relies on completely functional composting, like the soil in a forest is doing.