Open Snapchat
Tap the Chat icon
Open the conversation
Press and hold the message you want to erase
Tap Delete
Tap Delete again to confirm
To clear a whole conversation, press and hold the chat in the Chat list
Tap Chat Settings
Tap Clear from Chat Feed
Tap Clear to confirm
To delete saved messages, press and hold the saved message
Tap Unsave in Chat
Tap Delete if available
To delete your account messages from Snapchat servers, go to Snapchat Account Portal and delete your account