How do I access my iCloud Private Relay mail on iPhone?

It isn't clear what you're asking. Private Relay isn't directly related to email.

Are you referring to email aliases created by the Hide My Email feature? if so, you can see your setup via Settings -> iCloud -> Hide My Email

Here you'll see a list of email aliases you've setup, and the sites they relate to.

However, that doesn't preclude you from seeing mail sent to those addresses. Apple will automatically forward them to your regular iCloud account mailbox. Pretty much the only reason to use the Settings is to delete an address you no longer want to use.

If you are referring to Private Relay, it's controlled via the same Settings -> iCloud interface. It acts more like a proxy or VPN service that redirects all your traffic through Apple's servers to help obscure your actual location/IP address from sites you visit.