We have only just signed up for Cloudflare, and currently run a Magento Store on our server (https://www.carmats4u.com). We also have an account with Zenstores which communicates with our server via API.
If I select Test Connection on the Zenstores website it throws up the following error:
Magento returned: [Errno 1] _ssl.c:510: error:14077410:SSL routines:SSL23_GET_SERVER_HELLO:sslv3 alert handshake failure
Yet if I disable the proxies under DNS everything works fine.