The solution is further down the same page:
https://github.com/jedisct1/dnscrypt-proxy/issues/98#issuecomment-62636551
I had a problem flashing the zip (made by qwerty12) in the link so you may need to extract the contents to the relevant directories (in /system) and make sure they have the correct permissions. I used Fx explorer for this. You obviously need root to do all of this. Then set the DNS to 127.0.0.1 (I used Static DNS for WiFi but many programs will do this) That's all it should take. I have posted in the same github link confirming it works fine.
edit: No problem. I should mention that if you have trouble with setting the internal DNS to 127.0.0.1 (as I did) you may find it easier to just add the following to the 99dnscrypt file that is placed in the init.d folder. (add the following line to the end of the file, there should only be one other line in the init.d file anyway, the one that executes dnscrypt-proxy, so add it after that line)
iptables -t nat -A OUTPUT -p udp --dport 53 -j DNAT --to-destination 127.0.0.1
There may be a better way to do this (i.e. using something like AFWall with a custom script to switch the DNS to 127.0.0.1 when you need it) because this will affect your 3G connection (as it will expect to find a working DNS server, not 127.0.0.1) but it does work.