Greetings, Jenfrnd!
Thanks for reaching out to the Apple Support Communities! That’s a great question you have about printing text messages with a time stamp. If the messages are currently on your device, you’ll need to press the message and swipe to the left to view the time stamp. While the time is showing, in order to be able to print, you’ll need to Take a screenshot on your iPhone and print the screenshot from the Photos app on your device.
Keep in mind that if the messages are not currently on your device and are in a recent backup, it's possible to retrieve the messages by restoring from that backup. Please remember you would lose any content and settings added after the backup date. Use this link to Restore your iPhone, iPad, or iPod touch from a backup and then follow the steps provided to see the time stamps and create screenshots.
Have a wonderful day!