Apple - How to export and read .txt files using iPhone?

One solution would be to use Dropbox or iCloud to hold/sync your notes and read them with a simple text editing or note taking app. I use Byword.

Another solution is using Simplenote, and Notational Velocity.

Simplenote also has a web app at simplenoteapp.com.

These apps all automatically sync your notes and have great search features. I've used this for the past couple of years to store all of my notes.

Using Dropbox will be the simplest, free solution. Within the Dropbox app you can view text files. No other app needed.