CloudFlare has the second AMP cache. The first is provided by Google.
When viewing this page on a iPhone using the Desktop PC theme from Thesis / DIYtheme.com then the Cloudflare’s Accelerated Mobile Links works.
When viewing this page using Wptouch.com, the the AMP won´t work.
AMP test sites by TBT
CloudFlare demo pages
To see how it works, try viewing this post from your mobile device and clicking any of these links: