First, use the Cloudflare Crypto tab 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.
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.