Another view

I generally pass mine horizontally over a flame. Either a candle or the burner of my gas stove. I will do this to get all the fuzz off then soak several times in very hot , but not boiling, water. Soak long enough to let the water cool then take it out and wring the sling out by pinching the cords tightly between thumb and forefinger and squeezing along it's length. I do this a couple times. In fiber like hemp there is something in it that makes it naturally stiff, maybe pectin, though not sure... Squeegeeing the water out like this will make the this stuff come out with the water. The water will look brownish. Then back to soak again in hot water and repeat the squeegeeing process a few more times. Then dry like kid said. After all that if I wanted to I might rub in a light coat of beeswax in then rub it quickly in between the folds of a thick piece of leather until the heat from friction melts the wax and lets it soak in.
 
Kind of more info than you probably needed but maybe someone will find that helpful for later.

Looks like sisal to me. My standard treatment is to soak my slings in water for a minute and hang them on my shower curtain rod by the pouch with a weight tied to the the retention and release cord to keep them from twisting as the sling dries. It really softens the sisal. Part of the stiffness comes from glue added to the fibers as they're spun, and the soaking removes some of that. The rest will drip out as it dries, so put a cloth scrap or a towel under the sling.

It's just a singeing process. Actually if you have a thick piece of stubble it will catch fire for a sec but quickly go out as soon as it burns. It's generally safer to singe on cords that are thicker or tightly braided since the more surface area exposed the more chance that too much will burn too quickly though I don't think that is likely to happen or even be a problem.  
 
As far as soaking without burning goes I'm guessing it will work. I don't use sisal but if others here say it makes a big difference with soaking then it should work.

Quote from Thearos on Aug 2^nd, 2011, 4:40am:

I have one sling that I singed before soaking and one that I didn't singe at all and there isn't any difference in suppleness between them. You can soak your sling without singing it, though it looks like you've already singed it.

And here's another one, with the rest of the spool of ??sisal, with a split pouch.