They have a product for that https://www.cloudflare.com/pg-lp/speed-up-wordpress-with-clo... It caches all pages on Cloudflare and only bypasses Cache on Cookies such as `wp-.|wordpress.|comment_.|wordpress_logged_.` which is used by /wp-admin/ are and when someone posts a comment. This turns your WP into static without doing anything special. Or you can write a custom cache rule for cookies using "Page Rules" or newly introduced "Cache Rules" beta https://developers.cloudflare.com/cache/about/cache-rules/

Also check - a WordPress plugin for static site generation and deployment https://github.com/WP2Static/wp2static