I know the Batsuit has had many incarnations but what's it made of?
A chronological list is fine. The original can't be Kevlar it wasn't created then.
Origin was basic fabric, with ballistic vest sewn in.
The basic foundation of the Batsuit is a tight-fitting bodysuit, similar to many superheroes. In early depictions, contrasting briefs are worn over a unitard or union suit, similar to the garb of early 20th century circus performers. Batman #1 revealed that there is a ballistic vest sewn into the costume. In modern depictions, the briefs are integrated into the main costume, so that section of the costume constitutes only a seam and color change from the rest of the suit. The bodysuit has varied in color and style as depicted by different artists: grey tights with dark blue briefs, light blue tights etc.
The Post-Crisis version of the bodysuit is not constructed from simple fabric, but from fictional advanced materials that gives it resistance to tearing. In addition, the suit also contains various defense and protection mechanisms layered into the suit's fabric. The basic version of the Batsuit is insulated against electricity and is mildly fire resistant. Batman utilizes many different body armor designs, some of which are constructed into his Batsuits, and others which are separate.