You can clear your copy of a message thread on demand at any time. It is not possible to for you to clear message threads from the devices of people you are messaging with.
iOS
To clear your copy of a message thread:- In your Messages list, swipe the conversation thread you want to clear to the left
- Continue swiping when the space beside turns grey and a mute icon appears
- Release when the space beside turns red and you see a trash can icon appear
- Tap Clear Conversation to confirm
Android
To clear your copy of a message thread:- In your Messages list, press and hold the message thread you want to clear
- Tap Clear Conversation to confirm