"Cloth" that's edible (or even better, yummy)?

You can press cotton candy into a thin sheet that resembles paper or cloth. Put the candy between two pieces of parchment, flatten it with your hands and cut into shape. Consider that the sail may be delicate or very delicate, depending on how thick you make it. To attach it to the mast use caramel, isomalt, couverture, marzipan ...

El Bulli used to serve 'Flower Paper' made with this technique. Watch https://www.youtube.com/watch?v=oLpTCN9pT2Q to see a Demonstration (Flower Paper starts around 6 min 30 sec).

Did a bit of digging and found this archived thread from Cooking Light.

Pulling suggestions from stuff I saw on that thread and my own thoughts (full disclosure, I haven't tried any of them myself):

1. Melting sugar/corn syrup/some other sweetener and then letting it dry into a thin layer on a sheet pan. Then you could cut/crack part of it into a triangle and you have a stiff sail. It would probably support its own weight, but might be too heavy to hold on the "mast" and would probably be partially transparent.

2. You could try making gumpaste, which is supposed to harden into a relatively stiff structure. Not sure if it'd hold up its own weight over a few days, but wouldn't be hard to test it ahead of time.

3. The fruit rollup suggestion in the thread I linked above would be easy, provided you don't mind a neon-colored sail :)

Besides the suggestions from bgottfried91, one other possibility would be to use rolled fondant, especially if you wanted something closer to white:

Roll it out thinly, cut it to shape, then set it on a form to harden. This might take a couple of days to harden fully, but you can also put it into a pre-heated (but off) oven to dry it out. (note that it'll be soft when it comes out, let it cool to harden).

Thickness will affect the weight (and how much strain it'll put on the mast), but thicker will also mean it's more durable and better able to support itself.

...

If you have a silicone mat or parchment paper, you could also try a few other things, but they're going to be more brittle:

• Oatmeal lace cookies. (mostly sugar and butter, with some oatmeal & flour as a binder). They spread dramatically when you bake them, but you can lay them over something to shape. You'll also want to clean up the edges or lightly score them while they're still warm, so that you can achieve the shape you want. (this is rather similar to bgottfried91's first suggestion, but might be a little more forgiving than typical sugar work).

  You can do regular size lace cookies without parchment by letting them cool for a couple of minutes, then popping them back in the oven to soften enough to release ... but I wouldn't suggest it on something of significant size. (cupcake-sails, maybe ... not for a large cake, though).

• Cheese crisps. Sprinkle a relatively low-moisture cheese in roughly the shape you want on your parchment or silicone, bake in the oven 'til you drive off the moisture and most of the oils ... then you can drape it over something to let it cool. (and again, might want to score it while it's still warm)