Login to your server via SSH with root user and navigate to cPanel directory.
Download the CloudFlare package to your server.
curl -k -L https://github.com/cloudflare/CloudFlare-CPanel/tarball/master > cloudflare.tar.gz
Extract the CloudFlare package.
tar -zxvf cloudflare.tar.gz
This will extract a directory with UNIQUE_ID. This directory should look like following.
cloudflare-CloudFlare-CPanel-hsI96dg6 // Here unique ID is hsI96dg6
Navigate to cloudflare directory and install it in following format.
cd cloudflare-CloudFlare-CPanel-UNIQUE_ID/cloudflare // Replace your unique ID.
./install_cf API_HOST_KEY mod_cf "Your Company Name" // Replace following details. API_HOST_KEY == You will get this from your CloudFlare panel. Your Company Name == Hostname of your server. mod_cf == It is optional. If set, the installer will try to install mod_cloudflare
CloudFlare plugin installation may take between 30 seconds to 5 minutes. When installed, you will receive a message like "CloudFlare module installed successfully" and you would see an icon for “CloudFlare” in cPanel accounts.