One thing you might not know is that twill is a weave, not a fiber. That is, you can get twill weave in cotton, in wool, in linen, in synthetic, in blends...
Understanding the type of fiber used as well as the weave is instrumental in selecting an adequate material for a specific purpose.
My preferred material for capes and cloaks is usually some sort of midweight fine wool suiting. Sometimes, yes, these are in a twill weave. You could use a cotton twill (may be referred to in general as a "bottomweight"), but I find these tend to be a little stiff for a cloak. I find wool has a nicer drape at the equivalent weight. Wool suiting can be a little more expensive, however, so you may prefer a synthetic.
Pictures and tutorials from my costuming portfolio at Syagria's Cosplay Site!
Star Trek Original Series Uniform!
Original Creation for AB13
Most Recent Con:
PAX East, Anime Boston 2013