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, tap More, select the messages, then tap the trash icon
Tap Delete Message or Delete Conversation to confirm
Go to Settings
Tap Messages
Tap Keep Messages
Select 30 Days or 1 Year if you want old messages removed automatically
Go to Settings
Tap Apple ID
Tap iCloud
Turn off Messages in iCloud if you do not want messages synced back
Delete the conversation on all devices signed in with the same Apple ID
Empty Recently Deleted if available in your iOS version
Remove message attachments from Photos, Files, and other apps if they were saved separately
Erase the iPhone completely if you want all messages removed from the device
Go to Settings
Tap General
Tap Transfer or Reset iPhone
Tap Erase All Content and Settings