I got curious about how much fabric weighs, so I pulled out my postal scale and some one-yard pieces of batik I bought the other day. Four yards of batik weighed about 1 lb.
The $12.95 flat rate international priority box has a limit of 4 lbs on it. I'm not sure how much the box weighs, but theoretically it would be possible to ship about 15 yards of fabric that way. I'm just not sure that 15 yards of fabric would fit into the box.
If I think of it, next time I'm at the post office I'll see if I can pick up one of those boxes to see how much fabric will fit inside.
Edit: I just realized the same flat rate boxes are used for both domestic and international use, and I have one of the boxes here. I'm going to see how much yardage can be packed into it and post later!