How do I delete chats?

Clear the whole data on the app and don't restore your data

Delete Multiple Messages from iPhone
1. Go to Messages app from the home screen.
2. Tap "Edit" button on the top-left.
3. Select the messages you want to delete.
4. Click the Trash Can icon on the bottom-right to delete multiple message.
Delete a Specific Message of One Person
1. Enter the conversation that has the messages you want to delete.
2. Tap and hold on a message until the menu pops up. Then tap More.
3. Next to each message, a small circle will appear.
4. Tap the circle next to the messages you want to delete, tap the Trash Can icon on the bottom-left to delete the individual messages.
Delete Old Messages from iPhone in Settings App
The new iOS 8 allows you to delete all old messages on your phone all at once.
1. Go to "Settings" app from the homepage.
2. Go to "Messages".
3. Scroll down to "Message History". There are three options: 30 Days, 1 Year, and Forever. You can choose to delete all messages older than 30 days, or all messages older than a year old.
4. Confirm that you want to delete the old messages and attachments by clicking the "Delete" button.

How to Delete Messages on iPhone 6 Plus

Great resource for how to delete texts here with pictures.

How to Delete Text Messages From an iPhone