Weird. I thought that I had posted, already ...
The material is generally believed to have been coarse nylon. (Not rip-stop nylon or stiff nylon.)
Coarse polyester might also work, but if the material is too thin you will have to double it up or it will be too transparent. I used a polyester shower curtain from IKEA for my flak vest (actually, I made four vests from one shower curtain)
Most flak vests were replicas of a vest from a high-altitude suit, of which the original was also seen worn by a spaceman in the Cantina. The original is different in a few ways.
You will also need white leather, a black adjustment buckle, two insertion locks, 1" and 2" (or 45 mm) wide white straps, and something to fill the ribs with -- most people use PVC tubes. I used batting for fill out the small ribs.
I could send you a large ZIP-file with my collection of images if you PM me your email address.
One thing you should be aware of is that the vest is worn one way in ANH but another way in ESB and ROTJ.