I used to design and build reverse osmosis systems and waste water treatment plants.
Reverse osmosis membranes can not tolerate chlorine even a little bit.

To get rid of Sodium Hypochlorite (also known as chlorine or bleach), you can simply add an activated carbon filter / bed to your incoming water stream.

I'm not sure if wood ash would work. I believe it would get rid of some of the chlorine but I would be worried that it could raise the pH level of the water.
You can make caustic Potassium Hydroxide using rain water and wood ashes. (that knowledge comes from biodiesel experience)

If doing it on the cheap, I would remove some partially burned wood (black and crispy) and use that.

Hope that helps,

I draw a 5 gallon bucket and add one 500 MG Vitamin tablet . (ascorbic acid) . I let it sit overnight and then stir it up a bit .