Edit > Transform Path > Flip Horizontal/Vertical is grayed out if there aren't multiple layers in your document. In order to flip a path, you have to create an empty layer, flip your path, and then delete the empty layer. Please fix this unnecessary restriction.
i see... that's the first time i've observed someone try to flip a path that way. Usually cmd-t and then a right-click is how most do it. When i try it your way though, i get the same results as you... If you lock the layer, the options are greyed out too, so i can see why the background layer would behave the same. But in neither of those situations should the options be unavailable since the path is independent of the layer... weird.