You need root privileges on the web server in order to install mod_Cloudflare. SSH is about the only way to install mod_Cloudflare. If you’re having trouble logging in with SSH, your probably don’t have root access on that server.
As sdayman already said you need permissions to edit the web server configuration, and that is root via SSH (well, or directly in the console ), respectively the Windows equivalent.
That being said, mod_Cloudflare works beautifully, however considering Cloudflare does not support it any more and Apache “now” comes with its own plugin (mod_remoteip) I’d rather advise at this point to use mod_remoteip