Q: Are there any apps to provide time stamps on text messages on a phone that is not jailbroken?

The Messages app does this. Swipe left in the conversation and hold. You will see individual timestamps for each message. Release and the conversation returns to the previous view without timestamps for each message. This requires iOS 8 or higher.

all i can say is, no

As ember1205 already posted, every message in the iOS messaging app has both a date and a time stamp already. Merely swipe right-to-left to see the time stamp.

Also note that both of you were replying to a post from 5 years ago (so the OP was presumably using iOS 4 unless they'd just updated to the then new iOS 5).