I have done a lot of tests with CloudFlare and WordPress… CloudFlare is fine as CDN only, as it helps with Yahoo Yslow and Google Pagespeed ratings at GTmetrix. However, all of the other features of CF will cause problems if you are using plugins for caching, minifying and so on…
Try this…
Click on the DNS for the domain name in CloudFlare, Edit DNS it says, Click any of the clouds that are Orange, they will be greyed out if they are turned off.
Go back to the domain list, and choose CloudFlare Settings, you’ll be at the Settings Overview page, Disable everything except put the CDN to CDN only!
Security Settings Tab, Just turn everything off!
On the performance settings tab, for Caching level, set it to aggressive, and set Minimum expire TTL to 8 Days…
Turn off all 3 minify options, they will be greyed out and turn off Rocket Loader…
This is how I run cloudflare since I use PHP5-APCU full page caching with the WP-FFPC plugin, and Autoptimize for minify.
You can use the settings I provided as a start, then turn things on 1 by 1 in cloudflare if you need other options. Just be sure to purge the cloudflare cache after making changes and CTRL+F5 to clear your browser.
Hope this helps,
Chris