May I ask if you’re using some kind of a caching plugin for WordPress or not?
HTML isn’t cached by default as follows on the article below. We can set to cache it, however since WordPress you’d have some issues for end-visitors and would need to configure a way to “bypasss the cache on cookie”. Safer approach is to use plugin to create .html documents (files) of cached versions of your posts and pages, then web server will serve them by default and Cloudflare would cache as needed. I use W3 Total Cache for such case since it’s more advanced features to setup (even free version).
Any particular URL to share to test or? Is it CSS or JS file?
I’d suggest you to:
Disable RocketLoader
Set Browser Cache TTL to “Respect Existing Headers”
Purge Everything
Below article would help you to achieve the above and ease your further troubleshooting.
Just in case, upon changes make sure to clear all the cache at Cloudflare: