I quickly got the reply, that they are not responsible for content hosted by their customer, therefore they relay complaints to the ISP in charge of the IP address in question.
That is a bit weird.... isn't it?
I'm not sure if "getting impatient" will do them any good. A DMCA complaint is worthless if you aren't a US entity or do business in the US.
It's indeed a bit weird that Cloudflare doesn't respond to legal requests. But I don't know US law much, so I don't know how cooperative they have to be. They're probably going with the bare minimum, just so they don't get into trouble...