The fabric is called 'tackle twill', and is used to put numbers and players' names on sports jerseys. More info can be found here:
http://www.thedentedhelmet.com/showthread.php?t=6330&highlight=vest+material
Unfortunately, this fabric cannot be bought 'off the shelf', and therefore had to be special-ordered (even the color is considered a 'special' color, I think). I've E-mailed BobaFettish, who has been the contact for fabric orders in the past. Hopefully, he'll put up a new fabric order here soon, as I do not have the contact info.