The basic issue comes from the different ways that Unity and Gnome Flashback integrate input methods with Unity using Text Entry settings and ignoring
ibus-setup, while Gnome Flashback still uses
First let me say that I'm using 14.04. In Unity, I can add pinyin through Text Entry. When I login with Gnome Flashback, pinyin is indeed not available from Text Entry as you say. But input method switching from the menubar indicator still shows pinyin and pinyin entry works fine.
If this is not the case for you in 13.10, you can add pinyin entry from Gnome Flashback, but it works a little differently.
Don't use Text Entry. Rather, use
ibus-setup in a terminal (the gui looks a little different that it used to, by the way).
Go to the Input Method tab, click Select an Input Method, and scroll down to Show All Input Methods. You may need to click Select an Input Method again, but this time when you scroll down, you will see Chinese. When you highlight Chinese, pinyin and other input methods (depending on what you have installed) will popup on the right; but pinyin should be there by default. Choose the one you want.
In 13.10, integration of input switching into Text Entry and the use of the new version of
ibus-setup was still something of a work in progress; so it's possible that you are experiencing a bug. But either following the above method with
ibus-setup in Gnome Flashback or upgrading to 14.04 should provide a workaround for you.