I am not sure if Hostgator supports any Free SSL. However, there is a tweak which can help you using SSL on all your domains using Cloudflare.
Follow these steps, Remember Cloudflare should be completely disabled first.
Step 1- Go here - https://www.sslshopper.com/ssl-checker.html
Enter your domain, if Hostgator has installed a shared/self-signed SSL on domain(It is usually done in every hosting company), It doesn't matter if it shows errors inside SSL.
Step 2 - Go Back to Cloudflare >> Enable it.
Go to Crypto, SSL Settings and Change SSL type to - Full, Please make sure it is Full only and not Full(Strict).
This will enable you to access your website over a trusted SSL from Cloudflare. And Cloudflare can also fetch your website over HTTPS even if that certificate isn't valid. It won't create a problem for you.
If incase in first step, it shows that Port 443 on your server is closed. You will need to ask Hostgator to install a Shared or Self-Signed Free SSL on your domain. They will most probably cater to your request.