I got asked to design a filtering device that could filter a mixture of flour, rice, sugar and peanuts.?

Pretty simple, really. Make a long, vibrating incline, consisting of, say, two foot sections, with progressively larger holes in each section; the first would be very fine holes, for the flour, then, a section with holes slightly bigger than sugar granules, then holes that the rice will fall through, and the peanuts could just fall off the end.

Have you ever seen one of those gadgets they used to use for sorting coins in banks? You could use the same principal gradually making each layer smaller so that all will remain on their level according to size,i.e. largest stays on top,smallest make it to the bottom.