If you Google cloudflare settings for wordpress you will find a lot people giving tutorials how to speed up sites using Cloudflare. Let me tell you all of them are bullshit; the more you optimize the more problems you’re gonna face.
Here is the settings that I use where you won’t get any cache problems while keeping the Cloudflare security.
Crypto -> SSL = Full
Speed -> Auto Minify = Untick everything (JavaScript, CSS & HTML)
Speed -> Rocket Loader = Off
Caching -> Caching Level = No query string
Caching -> Browser Cache Expiration = Respect Existing Headers
Caching -> Always Online = Off
Firewall -> Settings -> Security Level = High
Firewall -> Settings -> Challenge Passage = 15 Minutes
Disable Cloudflare Caching
Cloudflare caching is the most terrible thing. That is the culprit of most problems. If you are like me who hates Cloudflare caching then create a Page Rules in Cloudflare with the path *example.com/* and select Cache = Bypass
This rules will apply on the domain including all of its sub domains. For example:
example.com www.example.com subdomain.example.com
Thanks to sdayman who helped me to achieve this.