You can implement HTTP/2 Server Push in any site, WP or not, that is proxied by Cloudflare by just adding a properly formatted Link header:
If you want to preload all CSS and JS files on a WordPress site, you can do so by installing and activating the Cloudflare Plugin, and adding a line of code to the wp-config.php file:
However, if your page has a large number of preloaded files, it may not render properly on Safari for iOS (my experience) and perhaps other browsers. This also may cause battery issues for mobile devices, so test it before final implementation.
I tried to enable server push with the plugin, but i seemed to me it was delivering two version of the same files. One pushed the other not. I am guessing this has something to do with plugin caches… Maybe not.
Have not been able to find a work around for this as yet.