How Can I Open the Table in My Favorite Editor Without Saving?

Opening the document in another editor without saving isn’t possible. You have to put the document onto your hard drive so another app can get the contents.

If you want to use TableFlip as a temporary scratchpad, copy the table as Markdown to your clipboard. Use the menu item “Edit > Copy Table…”, or the shortcut ⇧⌘C for this. Then paste the content it into your destination app.