You can have Siri check and read your emails for you from your iPhone just by asking “Do I have any new emails? If you do, Siri will give you a quick summary of them and you can tap on any of them to read them.
If you want Siri to read your emails for you from your iPhone, you can just say “Read my email” and she will begin reading them from the newest first. If you only want a particular email read, you can say “Read my email from __________” and fill in the blank with the name you want of who sent the email you want to hear.