I can't imagine sewing an edge on burlap. It tends to move because it is so loosely woven. If they just want rectangles, I would straight stitch the outline shapes into the burlap BEFORE cutting. This will at least make the edge more stable and you can fold the stitching in and fold another 1/4 inch over on top of it and stitch again.
Another idea would be to sew a narrow piece of matching trim to the underside to make a stable edge and pull a couple of string off around all the edges beyond the trim to form a fringe edge.
Another thought is to buy the narrow fusible strips that you can iron on to to fuse the folded edge but you would have to protect your ironing surface in case the fusible leaked through the open weave.GOOD LUCK!