I keep dental floss in all of my kits and also pack it into the survival kits I sell for classes. I use the Gore Glide also, as it was the toughest stuff I informally tested a couple of years ago. The no-shred varieties are much stronger than regular floss. It can be very difficult to work with when your hands are frozen (which is why I pack disposable handwarmers in each kit, too. Can't use your hands? Can't survive, then). I've used it for making all sorts of kit and also for shelter building, which it's plenty strong for when you're just tying supports that are leaning up against each other. It floats so if using it for fishing you need sinkers.
You can buy Glide in small rolls for about $1 at Wally World, Target, etc. Take it out of the case and it's pretty compact. You can buy the 500 yd. rolls also for about $8. I take a plastic credit card and wrap Gorilla Tape around one end and cut notches to store floss on the other end. The one in my wallet has about 4-5 feet of tape and about 20 or so feet of floss. The one in my mini kit has about 12 feet of tape and 30 feet of floss. The one in my car has about 25 feet of tape and 50-60 feet of floss on it. It's a compact and easy way to carry it.