Yes you can share the extensions and if you create the share link and open it in new browser window (maybe use private session window) then you navigate to the flash card extension, open the extension expanded (maximized) and then you copy the link that is in the browser address bar. That link points directly to that flash card extension.
The only issue with this the flash card extension can still be closed and users will see all other extensions you have enabled for that table. So if you don't want that you may need to create a synced table (or linked table + automation to auto-link records if you like) and only add the flash card extension to that table.