text-scale-mode-amount is what you want to save. But it is buffer-local. I don't think Desktop restores buffer-local variables, but if it does then it should already be working for you, I would think.
You can of course set the default text-scale value, i.e., for all buffers, to some value in your init file, if you want:
(setq-default text-scale-mode-amount 1) ; Or 2 or whatever.
But that's not the same thing as saving, for each buffer, its last value.
Another approach, since you mentioned frames, is to zoom the frames, not buffers.
You can zoom either frames or buffers using the commands in library
zoom-frm.el. You can in fact use the same commands to zoom either a frame or a buffer. You can use mouse buttons (e.g. with a modifier), keyboard keys, or the mouse wheel.
When you zoom a frame the
font frame parameter changes to have a larger or smaller size.
Dunno whether Desktop saves all frame parameters. I believe it saves some, at least. If it saves the
font parameter (and I think it does) then all of your zoomed frames should be restored at their last zoom levels in your next Emacs session.