I've forked the famous ddclient project and incorporated changes described by Peter R's blog to create a single easily installed application.
I wanted a few very simple installations to get things working, so here they are:
$ wget https://github.com/danielheth/ddclient-for-cloudflare/tarball/master
$ tar -xpvf master
$ cd danielheth*
$ sudo ./install.sh
Then follow the prompts which will help you configure ddclient to work with your cloudflare account.
ddclient logs to syslog... so using the following command can help you troubleshoot what's going on:
$ cat /var/log/syslog | grep ddclient
Your configuration is saved to the /etc/ddclient/ddclient.conf file in case you need to make any changes. It is locked down to root access.