I want to send an entire text feed from one of my contacts to my email address.

Hello lygsteven ,

Welcome to Apple Support Communities!

I understand from your question that you want to forward your messages to your email. I can certainly help you with this!

There is currently not a way to do this. The easiest way would be to take a screen shot and email the picture.

Take a screenshot on your iPhone

I hope this is able to resolve your issue. If you have any more questions or this does not resolve your issue, please reach back out on the thread!

Cheers.