I recently configured Cloudflare for a client and the performance results were indeed promising. On a very first view, it looks like a well developed product with interesting features. We came across a major checkout issue though. In some browsers, the buttons in the checkout did not work – hence, many people could not order. It was hard to debug as I could not reproduce the issue in the first place, but I finally managed to find the root cause.
My solution was simply to create a page rule in Cloudflare and disable the Rocket Loader for all pages like
https://www.domain.tld/checkout/onepage/*. This is probably a good idea anyway since it disables a beta feature on the very critical checkout pages.