Open the Messages app
Tap Edit in the top-left corner
Tap Select Messages
Tap the circle next to each conversation you want to delete
Tap Delete in the bottom-right corner
Tap Delete Messages to confirm
To delete a single conversation, swipe left on the conversation
Tap the trash icon
Tap Delete 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
Tap Delete to confirm
To delete messages automatically, go to Settings
Tap Messages
Tap Keep Messages
Choose 30 Days or 1 Year
Tap Delete to confirm when prompted
To delete all messages from iCloud, go to Settings
Tap your name
Tap iCloud
Tap Messages
Turn off Messages in iCloud
Choose Disable and Download Messages or Delete from iPhone when prompted