Open the Messages app
Find the conversation or message you want to delete
Swipe left on the conversation and tap Delete
Or open the conversation, press and hold the message, then tap More
Select the messages you want to delete
Tap the trash icon
Tap Delete Message
To delete multiple conversations, tap Edit in Messages
Select the conversations
Tap Delete
Confirm by tapping Delete again
To delete all messages from a conversation, open it and delete the conversation thread
To delete messages from iCloud, go to Settings
Tap your name
Tap iCloud
Tap Messages and turn it off if needed
To remove recently deleted messages, check the Recently Deleted section if available and delete them permanently