Frame or floor planks first?
Framing is typically build on top of the subfloor.  The finish flooring runs to within about 1/2" of the framing, then the gap is covered by baseboard.  The gap is supposed to allow for expansion and contraction of the flooring with changes in temperature and humidity; without the gap, if the wood swells, the only way for it to go is up, i.e. pulling away from the subfloor.

I think if you build your frame on top of the finish flooring, you also run the risk of having the weight of the frame press down on one end, causing lifting at the other, or pressing in the middle causing lifting at both ends.

EDIT: I've thought of another couple of reasons not to build your frame on top of the flooring:


2x4 lumber for framing comes in a few standard lengths: for example, 96" or 92 5/8" for 8" walls.  If you put the flooring underneath it, you're going to have to cut the 2x4's down by the thickness of the flooring so that your new walls match the height of the existing walls.
hardwood flooring is expensive! Why install it somewhere that you won't ever see it?