No, it (again) doesn't work like this at all. 1) DNS blocking of cloudflare is useless, you can receive IPs, or names in non-cloudflare zones, 2) IP blocking of the whole cloudflare will bring so much collateral damage (unrelated services going down) that it's a non-starter, politically speaking, 3) cloudflare is far from the only mass frontend / cdn available, there are hundreds high-collateral services out there.
Sorry I misunderstood the fact that you were talking about sending IPs and not randomly generated dns name from cloudflare. My question was does this app use use a custom protocal, and I'd define a pseudo random IP provider over push notifications to be a cudtom prptovol.
This is a nation state suppressing information, I don't see why wholesale blocking services like cloudflare or any of the other possible options would be a non-starter, given it only needs to last for a weekend. There also doesn't appear to be any evidence that this app uses any of these techniques either as far as ive sedn.