Liquid which neither dissolves in water nor oil I am looking for a liquid which is not miscible (or very close) with water or vegetable oil.  Ideally, I want to have a container which shows three layers (the three liquids) with clear boundary layers.

I was thinking that I should find a non-polar compound of very high molecular weight - such that difference in the density of that compound and oil is enough to draw it down out of the oil.  However, I haven't found it yet.

I would prefer a compound which is non-toxic and non-flammable if possible.

It feels like such a simple question, I must be missing something.
Fluorocarbons are compounds that are hydrophobe and lipophobe. It's a special property of perfluorinated compounds: They are non-polar and thus hydrophobic but in addition as the high electronegativity of fluorine reduces the polarizability of the atom, fluorocarbons are only weakly susceptible to the fleeting dipoles that form the basis of the London dispersion force. As a result, fluorocarbons have low intermolecular attractive forces and are lipophobic. 
I'm not sure about their toxicity, but this seems to be an issue, e.g. here.