As of August 5, 2014, CloudFlare supports WebSockets for Enterprise customers only. (Announcement)
WebSockets are currently only available for Enterprise customers, but will be available for other plan levels in the future.
All other customers -- Business, Pro, and Free -- should create a subdomain for Websockets in their CloudFlare DNS and disable the CloudFlare proxy ("grey cloud" the record in CloudFlare DNS Settings).
https://support.cloudflare.com/hc/en-us/articles/200169466-Can-I-use-CloudFlare-with-WebSockets-