After you enabled Cloudflare, your website might go in a redirect loop.
The reason for this is how SSL Support is configured with Cloudflare. The default setting is ‘Flexible’. Flexible means that SSL requests for your website will go via CloudFlare, and Cloudflare’s servers will attempt to access your website over normal HTTP. If you website is configured to open up using HTTPS this can create a loop.
In order to resolve this issue you need to change SSL Support for your domain from ‘Flexible’ to ‘Full Strict’. In this way after Cloudflare receive a secure requests for your domain, they will use another secure request over HTTPS to fetch it from its server.
You can change the SSL Support settings from your cPanel -> Cloudflare -> Settings tab. Once you change the value, please allow some time for it to work.
You can also read more about the different Cloudflare SSL Support options here.