You can change vibration settings by opening the Settings.app and selecting the "Sounds" option. The two first options are "Vibrate on Ring" and "Vibrate on Silent". Turn these off to disable all vibrations. However, this will disable vibrations system wide for all apps, not just Messages.
To get as close as possible to disabling vibrations for just the messages app:
- Open Settings.app and navigate to "Sounds" -> "Text Tone".
- Scroll to the top of the page and select "Vibration"
Scroll to bottom of page (under "Custom") and select "Create New Vibration".
Note: you can't create 0 vibration as you have to tap to start the "recording". However, you can tap it very lightly to start the "recording".
Tap the screen very lightly and let the recording go until it stops. Like I mentioned, it is perfect, but very close - especially if you tap very lightly.
- Save the Recording (something like "Minimal Vibe") and assign that to you text tone vibration pattern.
Keep in mind, it is possible to override that vibration pattern when you set custom ringtones or vibration patterns on individual contacts, so if it isn't working quite right for you for certain contacts, be sure to check those settings. Or, the alternative would be to set the "Minimal Vibe" settings for just some particular contacts.