Check out this tutorial on all the details of setting up Apache to serve content using SSL. Namecheap also provides their own documentation. Essentially what you need to do is upload the certs and add a new VirtualHost to your Apache config. Something like:

<VirtualHost *:443>
    SSLEngine on                                                                
    SSLProtocol all -SSLv2                                                      
    SSLCipherSuite ALL:!ADH:!EXPORT:!SSLv2:RC4+RSA:+HIGH:+MEDIUM                

    SSLCertificateFile /etc/apache2/ssl/ssl.crt                           
    SSLCertificateKeyFile /etc/apache2/ssl/private.key                        
    SSLCertificateChainFile /etc/apache2/ssl/sub.class1.server.ca.pem 
    ServerAdmin webmaster@localhost

    DocumentRoot /var/www/html

    # Other configuration...

</VirtualHost>

If you could expand on the problems you faced using CloudFlare's flexible SSL, we might be able to help you.