I would like to make an heat exchanger using the flue from my 40 gal. water heater. The "heated" water would be used for the supply side of my water heater. Would this work and is there a concern about the flow of exhaust through the flue liner, 2 floors to the top?

Is your flue steel and your waterline copper? Not a great combination.
AO Smith has a couple of models of water heaters that the flue inside the heater coils around the inside of the tank to do what you are looking to do. (use the heat from the flue) I think Bradford White does also.
But to answer your question, if your flue is at least 4 inch and your furnace does not also use this flue you should be fine as far as sizing.
If you are looking to bring your feed water temp up why not put a holding tank next to your heater to allow the water to come closer to room temperature before entering your heater? Just don't have it so large that it becomes stagnant water and a breeding ground for nasty stuff like Legionairs Disease.

You may find this link interesting;
Energy Savers: Heat Pump Water Heaters
Good luck, Tom