I have to say that I disagree with the holding in this order. Upon receipt of a DMCA infringement claim, CloudFlare could program its edge servers to deny requests to the reported URLs. The fact that they could easily do this (but elect not to) and that if they did, it would probably (but not absolutely) prevent further infringing copies of the content from being made (even if the origin moved elsewhere) is sufficient to convince me that they are potentially liable for contributory infringement. Sometimes you have to work backwards from how the technology works to come to the correct conclusion, but the judge clearly failed to do that here.
The fact that such a denial wouldn't necessarily block access to the content at the origin server is irrelevant. Moreover, the holding also inexplicably ignores the fact that many origin servers only allow access to their desired CDN anyway. This is actually a very common configuration to avoid having the origin server being DOSed.
If I were the plaintiffs, I would almost certainly appeal this ruling to the 9th Circuit - and after hiring a much better attorney.