In order for Cloudflare (or anyone) to be a part of this program they have to comply with a particular set of rules.

Limiting data. Your DNS data can reveal a lot of sensitive information about you, and currently DNS providers aren’t subject to any limits on what they can do with that data; we want to change that. Our policy requires that your data will only be used for the purpose of operating the service, must not be retained for longer than 24 hours, and cannot be sold, shared, or licensed to other parties.

Yes, governments can secret around this with intelligence orders, just like they can do with any of the ISPs that will keep all of the data indefinitely instead of for 24 hours.