You will want to be sure the DNS records you have with Ezoic match the DNS records from your host.
When integrated with Ezoic via the Cloudflare method, Ezoic is acting as the main proxy for your site rather than Cloudflare. This means that any DNS updates required to match the records found at the host need to be made within the Ezoic Dashboard first (Ezoic Dashboard > Settings > DNS Records). These changes will then automatically propagate into Cloudflare. Note: This will not work the other way around as any changes made at Cloudflare would just be overwritten by Ezoic.