When you delete your message history, this is deleted from Gmail and classic Hangouts on all your devices.
If you use Google Chat and not classic Hangouts, visit Turn history on or off in Google Chat.
Important: Google Hangouts is now Google Chat. You can no longer access Hangouts on mobile devices or the web. Learn about the switch from Google Hangouts to Google Chat.
Important: You can no longer download the classic Hangouts app. If you delete or uninstall the classic Hangouts app on your Android device, you aren't able to reinstall. To continue your conversations, move to the Google Chat app. Learn about the switch from classic Hangouts to Google Chat.