It would have been good to know/ have this context when you were attempting to add Cloudflare to your root hint servers and I suggested you should be using forwarders in a previous thread. Forwarders are used for specifying a recursive resolver for resolving host names for zones which don’t exist in your internal DNS. Based on your description you have configured your internal nameserver to be authoritative for one or more zones. Forwarders don’t ask external servers for how to resolve a zone the local DNS server is authoritative for, nor is that the purpose of a root hint server. If a DNS server is authoritative for a zone it responds authoritatively… it doesn’t ask anyone else because it is the source of truth for DNS resolution.
The Cloudflare servers which are authoritative for zones on Cloudflare (foo.ns.cloudflare.com and bar.ns.cloudflare.com) are not recursive nameservers. That means that even if you could get what you are trying to do to work you would only be able to resolve zones in your DNS or hosted by Cloudflare. That would … for example prevent your users from resolving google.com.
An appropriate forwarder from Cloudflare would be 188.8.131.52 and 184.108.40.206 as those are public recursive resolvers. However, that still won’t help with resolving hostnames which are related to zones your authoritative internal DNS server claims to be authoritative for but does not have.