The bat-suit is one of the most highly advanced technological items in comics, the more so that it maintains an aspect of realism to it with the more contemporary aspects of technology and science applied to it. There is of course still an aspect of fantasy, but the tech itself is a little misconstrued as well. Here are a couple of reasons why.
Both of these materials are not exactly still considered new by today’s standards (Nomex has been around since the 1960s) but they are still used in a lot of apllications. Nomex is still used by a lot of firefighters and Kevlar figures heavily into body armour. What most don’t know is that they are chemically very similar, both being aramids similar to nylon. What is not really of any value is weaving the two together as is usually described about the bat-suit. The two materials work on the concept of their uniform nature – Kevlar is effective because its tensile strength along a horizontal surface is quite high, high enough to stop bullets, while Nomex is a poor conductor of heat. The problem is mixing the two together is going to create a problem akin to trying to stop the wind with a screen door. Assuming the fibers are woven one for one it means that that every second fiber is not designed to do what the overall effect desires. I guess they could say that it was just layered, but that leads to another problem, that of suffocation.
Magical Kevlar … there is nothing it can’t do. Apparently by putting Kevlar in the cowl it makes Batman be able to be shot in the head. That is not exactly how Kevlar helmets work though. Kevlar does essentially one thing, it stops something from getting through by having a high friction on a perpendicular plane to its surface. This eliminates the problem of penetration (which is an important one when it comes to most organs) but not of momentum. A lot of people while wearing armour and if hit by a bullet will still get a broken ribs because the bullet’s momentum continues even if it doesn’t penetrate the material. In the case of army helmets this means that the helmet has the ability to move around on the head somewhat to dissipate the shock. In terms of a skin tight helmet this would be mostly useless. It might stop the bullet, but the momentum would probably still result in skull fractures and concussions.