Open the Messages app
Tap Edit in the top-left corner
Tap Select Messages
Tap the circles next to the conversations you want to delete
Tap Delete
Tap Delete Message to confirm
To delete all messages in a conversation, open the conversation
Tap the contact name or number at the top
Tap Info
Tap Delete Conversation
Confirm deletion
To delete all messages automatically in the future, go to Settings
Tap Apps
Tap Messages
Tap Keep Messages
Select 30 Days or 1 Year
Confirm when prompted
To delete all messages from iCloud, go to Settings
Tap your name
Tap iCloud
Tap Messages
Turn off Use on this iPhone
Choose Disable and Download Messages or Delete from iPhone, if shown