The vase is not developable, but if it is sliced horizontally in several places, each band approximates a frustum.
Each frustum can be unwrapped, and Swept to several surfaces, next to each other, and pattern applied.
Then use Flow on each band arc surface to the frustum bands of the vase, and I suppose project onto the vase object...
Its like the wine bottle label thread...

- Brian

I'll have to try some slicing...