should i wrap exhaust duct joints of hot water heater?

Duct tape and flexible ducts are OK for a fume hood exhausts or for ventilation ducts, but not for combustion exhausts.

Although regulations depend on where you live, for your own safety I would not use a flexible metal duct for combustion exhausts as they are not designed for this and can be prone to leaking. Same goes for duct tape. The glue or tape could melt, or the tape could perhaps even catch fire from the hot fumes.

So, use fixed tubing and connect it as per the instructions, probably with screws. There are also systems that are self sealing with built in rubber rings.

Furthermore, if possible for your hot water heater, I would recommend that you also connect an intake duct for fresh air. This will lessen the amount of CO gas is produced, and make it less likely that the combustion exhaust product escape inside the house in stead of through the exhaust pipe. If you have a heater with condensation, it is possible you need to use specific concentric tubing to do this. It might be necessary to build a new connection to the outside for the intake, or, if the existing exhaust is wide enough, you could install an air intake tube inside the existing exhaust tube.

If the vent is not going into a masonry chimney or equal, Type B vent should be used ; it is double wall to lower the temperature of the outer surface. I recently put in a hot water heater and had to replace the original Type B because it could not be changed after 20 years to meet the new unit. I don't believe Home depot has Type B; try plumbing supply or Mcoys.