Yes, the chakin comes with a fair bit of starch in it, but vigorous rinse (and use) will take care of that quickly.
Traditionally you simply rinse the chakin with water, rubbing to get out any stains, rather than "washing" it. If you rinse soon after use, that's usually good enough. I guess you could wash it with laundry detergent or try bleaching it if you must, but that might break down the fibres a bit.
You ask why the Japanese would "choose something like this to pat dry a Chawan after pre-heating". It has to do with tea ceremony, and the way in which the chakin is folded, then opened out to wipe the chawan dry, and then refolded again for possible reuse. Take it from me, a floppy/limp chakin is harder to use
in that context than one that still retains a bit of stiffness!
If you're curious about how it's used in tea ceremony, see:
http://www.youtube.com/watch?v=7tt7NBIVeMY
The part where the chakin is used to dry the bowl is at 3:09 to 3:24. You'll notice that the host begins by wiping the rim/outer area of the bowl, then ends by wiping the innermost part. It's hard to see in this video, but when the host dries the bowl on the inside, she is simultaneously refolding the chakin back into the "loop" shape that is normally used when it's not actually being employed to wipe/dry a bowl.
