Mike,
I use the DeWitt boxes for this reason. I can see the flies in the box and not have to open the lid.
The flies are loose in the sections.
They are available in many combinations. For regular trout flies .
One l choose to use is app 7x3x 3/4 and has 18 compartments.
For larger flies, such as hoppers, stones etc there are options with 6 and 8.
They are very light, strong and float real well.
Boxes that hold dries by the hook, l dislike as hackles can be distorted, and nothing worse than a dry that does not sit right when being fished.
Davy