Cloudflare would have to bring that suit since they were the ones defrauded. The site owners probably can't sue Cloudflare because of their contract. So the site owners probably have to go basic "tortious interference" and be ready to show actual damages.
No, if the site owners have been harmed by Flock + Cyble knowingly filing a false takedown notice then they can sue Flock + Cyble. If Cloudflare's reputation has also been harmed then they could sue Flock + Cyble as well.
The "resulting damages" is pretty small though, they just had to move off of cloudflare. I'm not sure it would be worth it, especially if the other side doesn't end up paying their legal costs.
False accusation of criminal behavior is defamation and in many US states such accusations are assumed to be damaging. No evidence of damage is needed.