I need to be able to resolve one domain via a specific DNS server, while everything should be resolved by other DNS server(s). For example, resolve bbc.co.uk via 184.108.40.206 DNS server, but everything else by 220.127.116.11 . Is it possible?
You'll need to configure a DNS server that contains a forward lookup zone for example.com (I wouldn't mess with bbc.co.uk, sounds a little nefarious,) a forwarder to 18.104.22.168, and appropriate A and/or CNAME records.
Otherwise you might have an easier time changing the hosts file.