First, use the Cloudflare SSL/TLS app to enable “Always Use HTTPS.” That should provide a more consistent user experience.
Second, there’s some mixed content (Some of your WordPress resources are defined with HTTP.
https://support.cloudflare.com/hc/en-us/articles/200170476-How-do-I-fix-the-SSL-Mixed-Content-Error-Message-
Third (maybe optional), turn on Automatic HTTPS Rewrites. This might fix the mixed content problems, but it’s good practice anyhow to try to use HTTPS.
As a sidenote, when I type in www, either with HTTP or HTTPS, it redirects to non-www. This is good since it also provides a consistent user experience.