Now this was a new one on me, since I hadn't seen the burlap trend creep its way onto the cake flowers yet. I thought it was funny, though, so I figured out a way to burlap-itize the flower.
First, I rolled out some brown gumpaste and texturized it with an impression mat that had a woven pattern on it. This one was a Makins clay mat.
Next, I cut out the petals to make the flower. Don't they look lovely and texturey? You could also use this mat to make ice cream cones, that's what this reminded me of.
Take each petal and turn them upside down on the texture mat, then ripple and thin the edges. You can really rip into them since the edges of real burlap is generally pretty raggedy looking.
Take a little pair of scissors and chop up the edges a little to rag them up a bit.
From there, all you need to do is form the center flower, which can look more like a bundle of fabric pieces than a real flower, and dry the other petals so that they can be placed on the cake later. If you want to get more obsessively realistic you can take a small poky tool and cut some holes in the gumpaste to make it look like the holes in the woven fabric.
Brush the petals and the center flower with a little brown petal dust once they're all dry, and that will give your gumpaste burlap some depth.
Sorry that I can't reproduce the hairs that are on real burlap, we'll have to do without that. At least the gumpaste version doesn't smell like the fabric type.