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 remove
Tap the trash icon
Tap Delete Message or Delete All
Go to Settings
Tap Apps
Tap Messages
Tap Keep Messages
Select 30 Days or 1 Year if you want messages to auto-delete sooner
Delete the conversation from all devices signed in to the same Apple ID
Turn off Messages in iCloud if you do not want messages synced across devices
Go to Settings
Tap your name
Tap iCloud
Tap Messages
Turn off Use on this iPhone
Delete any message attachments from Photos, Files, or other apps
Empty the Recently Deleted album in Photos if attachments were saved there
Delete backups that may still contain old messages
Go to Settings
Tap your name
Tap iCloud
Tap iCloud Backup
Delete old backups if needed
Erase the iPhone if you want to remove all stored messages from the device
Go to Settings
Tap General
Tap Transfer or Reset iPhone
Tap Erase All Content and Settings
Sign out of iMessage on other Apple devices if needed
Remove messages from Mac, iPad, or other synced devices
Ask the other person to delete the conversation from their device if necessary