Most sporrans of this type have a rough outer edge. The edge is usually not "slicked".
Agreed. With a PV or acrylic kilt, it doesn't take much of an edge or rough surface to do a number on the fabric. As noted by artificer, the chain and catch can also be a problem, so check them for any roughness or sharp edges—or switch to a leather sporran strap.

If you don't feel confident taking a knife to the sharp edges of your sporran, you can purchase a small beveler at a fairly modest cost at any leather shop. Run it along the edge of a scrap of leather a few times to get the hang of it. After beveling, slick it up and finish it off with a bit of shoe polish to match the color of your sporran.

Finally, it looks like there is a knot in the stitching at the bottom of the sporran. If it is really rough, you can carefully remove a bit of leather under it and set it flush with a spot of superglue.