Fabric stores sell a micro-weave material very similar to the stuff used by HGW for their 1/32nd scale seat belts.
This doesn't always work so well in smaller scales, so I tend to use wine bottle foil, or similar foil from various packaging for 1/48th scale, with fine plastic rod, fuse wire and lead wire for the hardware, and where needed, punched plastic or cut rod for circular quick-release buckles.
If smaller than 1/32nd scale, any weave/texture will not be noticed, so I just paint the foil the required colour.