Your website is using Cloudflare’s Flexible SSL, which needs some more configuration on WordPress to work properly:
The fastest and easiest way to work around this is to use Cloudflare’s Full SSL with a self-signed certificate from our Free SSL Certificates tool; here is a guide:
Did you install the self-signed SSL certificate as in the guide I linked to? If you did now it’s a waiting game, where you have to wait up to 15 minutes (it might take even more) for the SSL certificate to work and to Cloudflare to detect it. In fact now I checked and it works!