Is there a way to integrate Cloudflare email routing for login and signup
Cloudflare Email Routing, as far as I understand, is simply a forwarding service for emails. There is no sending capability (see also https://community.cloudflare.com/t/how-to-send-email-using-email-routing/330400/4).
That said, Ghost uses nodemailer under the hood to send transactional emails. All transport options from nodemailer are available, but the easiest is SMTP. As long as an email provider you choose supports SMTP, you can use it for Ghost’s transactional emails.
Hello, Cloudflare’s routing service only offers the option of redirecting emails sent to your personalized domain to an email account that you use. And that’s it.
As for transactional emails, you should use an SMTP service. Ghost recommends Mailgun, but there are other options, such as Brevo, Oracle Email Delivery, Amazon SES and others. Of these, I really like Brevo. Very easy to configure.
There are also some guidelines in the Ghost documentation.