I need to setup an email address tied to a domain hosted on wp engine but purchased through a different registrar. The registrar is asking for the right IP address for Cloudflare as they will then setup email hosting for us.
Can this be done on the free account, or does it require something else? How do I get the right IP address and will I need to make any changes on Cloudflare?
It sounds like there may be some confusion among the parties involved in your email conversation. Setting up domain email hosting at a third party does not involve any Cloudflare IPs.
In order to receive domain email you will need to create at least one MX record that points to the hostname provided by your email provider. The following #tutorial covers how to add DNS records to your Cloudflare account.