Probably not the answer you're hoping for, but why do want to hide your real IP? If it's for general security I would just firewall off you server from IPs that don't belong to Cloudflare and call it good. If it's for other reasons (running legally questionable stuff for example) I would guess Cloudflare would give you up easily to law enforcement so not worth it there either.

Allow only these ranges:

    curl -s -X GET "https://api.cloudflare.com/client/v4/ips" | jq -r '.result.ipv4_cidrs[]'