Generally speaking Cloudflare is compatible with Easy Digital Downloads. Here are some issues and solutions we've discovered.
Cloudflare's ScrapeShield technology grabs the email address of the customer and obfuscates it so that spammers cannot scrape it and send spam.
The drawback to this is that it's then not a valid email address, and the customer becomes disconnected from the purchase.
Cloudflare offers instructions on how to turn off this feature. Once it's off then the issue is resolved.
HTTPS Protocol Rewriting
This option attempts to make all of your site's assets (like CSS files etc) load over the same protocol (http or https). Occasionally it doesn't load properly, causing downloads to be served without contents, so the filesize is 0. You can turn this feature off in your Cloudflare panel, Cloudflare's documentation on HTTPS Protocol Rewriting explains how.
Payments not marked as complete
If your payments are not getting marked as complete and you are using Clourdflare, see this document.