My opinion: USPS is tooting their horns about the flat rate boxes and envelopes, but I do a lot of shipping and I've found them too small or too shallow for what I ship. Even if they do meet my need in size, regular Priority rates (and free boxes/envelopes) always end up being cheaper to ship than a flat rate one.
For fabric, order some free priority tyvec envelopes. They are light-weight (but super strong), and the packaging, being so light-weight, adds less to shipping weight and costs than a box does.