A script you paste into the browser console on Facebook Messenger. It deletes whole conversations, the same way the three-dot menu does, until the list is empty or you press STOP.
Open the developer console with Ctrl+Shift+J (Windows/Linux) or Cmd+Option+J (Mac).
Paste the script and press Enter. A status bar with STOP appears at the top of the page.
This deletes entire conversations, not individual messages. Other people keep their copy. If Facebook rate-limits you, set a finite LIMIT at the top of the script.