The Bird Eats Bug browser extension can be used in incognito windows.
You just need to enable the permission in the extension management page. Here are steps to follow:
1. Go to the Manage Extensions page by pasting this link to your browser chrome://extensions/
2. Click on Details button on the Bird Eats Bug extension
3. Enable the toggle of Allow in Incognito
4. Now you can use the extension to record sessions in an Incognito window
Try Bird later, from your desktop