We are working on an online cinema project showing movies and TV series without violating content. We have movie content that we don’t own a license. I want to ask to your expericen what would Cloudflare do to DMCA complaints about copyright? are they going to raise complaints and stop our services or ignore them?
They are going to forward the notice to your host (and might share the host details) and - depending on the nature of the violation - may also suspend your service.
Keep in mind, Cloudflare is a US company and is bound to US law (which includes DMCA), even if neither you nor your host were subject to that.