Open Snapchat
Go to the chat or conversation
Press and hold the message you want to erase
Tap Delete
Confirm Delete if prompted
To clear an entire chat, go to the chat list
Press and hold the conversation
Tap Chat Settings
Tap Clear from Chat Feed
Confirm the action if prompted
To delete saved messages, open the chat
Press and hold the saved message
Tap Unsave
Then press and hold the message again
Tap Delete
To erase all chat history from your device, clear conversations from the chat list
To remove messages from both sides, delete them as soon as possible
Keep in mind some messages may still be visible if saved or already screenshotted