It is perhaps not correct to say that you cannot sign in. From what I can understand, you don’t want to or have not tried to manually configure the Windows Mail client; if you manually configure a mail client with the correct settings, it will work just fine.
What you then want is for mail clients to be autoconfigured and you invoked Virtualmin → Email Settings → Mail Client Configuration to that end . If you were using Virtualmin’s DNS then this is the only step you would need to take but you are using Cloudflare so you must take additional steps, naturally.
If you subscribe to Virtualmin Pro, you get Cloudflare as one of the DNS providers and you need take no additional steps to manage DNS records. However, If you wish to continue with Virtualmin GPL, you need to keep synced the DNS records in Virtualmin’s DNS with the records in Cloudflare.
Also see @MrPete’s addendum.
How to get nginx to support Mail AutoConfigure (or any other cgi-bin scripts)