Agree w/ others regarding size of both of your coops vs # of chickens you looking to have.
Here is another fly trap.
Ranch Pest Control
I'll have to do some more digging around, i know there are others as well. If you don't want to use pesticides.
One easier way to do your DLM, would be to put your coop (s) up on cinder blocks. Then put your litter in - part way up the cinder block height. As it breaks down, while digesting chicken waste, you add more.
If you can get mulch, as described previously by Aart, great. But so many more things... grass clippings, garden waste, the shavings from the inside of the coop, pine pellets (horse bedding), hay/straw (can be issues), shredded paper/cardboard/junk mail, pine straw. Smallish branches w/ nuts or pinecones. Leaves in the fall.
In a larger run set up, setting up any extra area for compost. You can put kitchen waste there. In your smaller ones, pretty sure you will not have the room...
Here is some of what I've done -
DLM.
I've had flies around the ponies (not many), but DLM seems to take care of flies in our coops/pens/runs... Even when I had juvenile chickens running in my raised beds, prepping them. There are many, many examples of DLM throughout BYC. You can search it.
Also, here is a great video. This is BeeKissed (not sure she's still on BYC)
DLM in hooped coop
LOTS of videos out there now. Everyone does DLM a little differently. Since you are already having issues with flies, using some other ideas for control good. One way to get wood chips or mulch is chipdrop or local arborists (i never did get chipdrop to work, but know others here in NC have).
Another issue - I can't remember for sure, but in your climate, you may also need to open gup more ventilation in both of those
TSC coops. Otherwise, they are nice!!
Took me a bit, probably others have shared this as well...
Edit to add - LOVE the flower mural on your privacy fence!!