Clearance ?

Should there be some clearance or flashing between the soffit hardy board and the exhaust vent for the furnace?

Yes there should be.
Hot flue and wood make fire and with zero support it must be touching.
Most gas flues require one inch space.

What type of furnace is it?

Did you see what type of pipe it is? there is some zero clearance flue pipe.

NFPA 54has info on flue clearances, but I believe PVC is the only allowed zero clearance flue.

Mid EFF. Conventional Gas forced air. 70k output BTU

Here is a link to some triple wall pipe,