I did a complete FAK revamp a year ago and found that if it's marketed as a "FAK bag," meaning lots of compartments/pockets, red exterior, a white cross and the words "First Aid" stenciled on the outside, the price goes up considerably. And often the online sources don't provide a decent look at the interior layout, a big drawback for me. Obviously your choice is going to depend on the amount and depth of the supplies you include.
Here's one of the largest selections I found for "first aid kit bags." But still pricey (I'm "thrifty").
My wife actually deserves credit for pointing me in another direction. She suggested I look at a soft-sided bag like she uses to carry toiletries/make-up when we travel. By their very nature, lots of compartments with clear sides to see the contents. eBags.com has a fair selection of kits on the small side — a couple
here and
here.
For a larger kit, you might consider soft-sided fishing tackle bags. Huge selection of sizes/configurations and by design, lots of compartments. Take a look at
Bass Pro's selection. Some include clear plastic compartmentalized containers which may or may not appeal to you. For one of my more recent smaller kits, I ended up using the #3 organizer bag
here from Outdoor Research.
You might look at soft-sided camera bags. All shapes and sizes with compartments at a reasonable price.