I use Cloudflare, quite happily for years, for my three WordPress sites. I recently received an email from them saying I should create a page rule to do a wild card 301 redirect to redirect my http protocol to https. (I already had SSL: Flexible enabled.)
The change is working fine -- I key in a http://mysite.com/... page and it redirects it to a https://mysite.com/... page.
But now I'm wondering about all my internal links on my WordPress posts and pages that begin with http. Do I need to do a search and replace on my site and change all the http to https?