The best deterrent is to keep your materials & flies clean. The "dirt", which is protein, that gets on the materials is what initially attracts them, and they will subsequently chew up the materials. I use moth crystals for some materials storage, and last time I had asked my wife to pick up some, she brought home a box that had small packets of moth crystals, similar to the silica dessicant packs used to pack electronics, cameras or other items that may be prone to moisture problems. The crystals don't smell good, but I've not had a problem with it, as I transfer flies from bigger storage boxes to smaller fly boxes for use & the smell dissipates quickly since the packets don't allow the chemical to come in direct contact with the flies.
I'll also use the silica packs in boxes of flies as it helps keep the moisture away from hooks, but I also believe it aids in deterring insects, as they need moisture to survive. Deprive them of any moisture & they tend to stay away.
I've also used ziplock storage bags & although prefer a good sealed tackle/fly box, the bags work well too as a quick & temporary option, particularly the heavier & thicker ml bags intended for frozen foods. In the past, I've had insects chew thru plastic ziplock bags that had become soiled & destroy some materials, so IMO, that's not something I want to rely on completely.
BTW, the chemical in the crystals is not the same as in the moth balls. The moths balls are a deterrent, but the crystals will kill most vermin & their eggs. However, I also store many materials in a freezer, which is the best long term storage option I've found. If you place flies in a freezer, add the silica dessicant packs to help keep the hooks from rusting.
