This article explains how to delete all Snapchat conversations from the chat page.
Steps
Step 1. Open Snapchat
The icon depicts a white ghost on a yellow background.
If you are not logged in, tap "Login", then enter your username (or email address) and password
Step 2. Swipe your finger from top to bottom on the main screen
This will open your profile page.
Step 3. Tap ⚙️ in the top right corner
Step 4. Scroll down and tap Clear Conversations
This button is located at the bottom of the "Settings" page, more precisely in the section entitled "Privacy".
Step 5. Tap Erase everything
This option is located in the upper right corner.
You can also tap the "x" to the right of each contact to clear only the history of conversations you have had with this person
Step 6. Tap Delete
Tapping this button will confirm your decision and the conversation history will be cleared.