The microbraid Kevlar from Pratt Hobbies is excellent quality, astoundingly strong and durable. It rolls up easily so it is easy to stuff into a small diameter tube. Because it is braided, it won't unravel.
I have also used plenty of Kevlar twine from BRS Hobbies, and I have been quite satisfied with it. Their twine is twisted, though, rather than braided.
I obtain my very lightweight (28 lb.) Kevlar from FlisKits. It resembles very thin thread and appears to be a monofilament, but in fact it is made from multiple hair-thin strands.
I have never found any Kevlar (aramid fiber cord or thread) in retail stores; the only places I have seen it were through online hobby and craft supplies vendors and on ebay.
As an alternative to Kevlar, I have also used 49-strand or 19-strand nylon coated stainless steel beading cord on occasion. You can find it at crafts stores like Michael's and Joanne's, and sometimes in the crafts section at Walmart. It is very fine (0.012", 0.015" and 0.018" diameters are available) and is very flexible. The 19-strand is marginally less flexible (the higher the strand count, the more flexible the cord) but it also works well as a shock cord or cord leash. Either kind is very fine in diameter, extremely smooth in finish, virtually kink-proof and extremely resistant to tangling. Avoid the more common (and less expensive) 7-strand steel cord; it is much stiffer and harder to work with. And by all means stay away from the type of metal beading cord called "tiger tail." The stuff is about as easy to work with as picture hanging wire.
A major brand is Beadalon. The 0.012" 19 strand has a breaking strength of 12 lbs. and is hair-thin; it works very well in Micromaxx models. I prefer using it over very lightweight Kevlar for such models because of its smooth texture and resistance to tangling. The 0.015" 49-strand has a rated break strength of 20 lbs. and works fine in most small to medium-sized LPR models.
Metal beading cord is more expensive per foot than most Kevlar that you can find (at least the stuff at Michael's is - 0.45 per foot
although you can probably find better prices for it online), but unlike Kevlar, it is something that you can run to the store and get if you need it right away. You can knot it, but a better, cleaner way to attach anything to it is to create a loop it it and then join the tag end to the line with a crimp bead. Braided stainless steel beading cord resembles bulk fishing leader, but it is finer in diameter, smoother in finish and has a softer flex. And you can find it at more retailers. The stuff is even more fireproof than Kevlar, too; in fact, nothing short of a severe cato will melt it, and it will hold up fine after exposure to many, many ejection charges.