Turn the water heater off and let it cool.
Drain water from the tanks completely, then refill halfway with fresh water.
Mix a solution of household bleach and water, ¼ cup of bleach for each 15 gallons of water, according to RVBasics.com. (See References 1.) Use regular bleach, not the kind with fragrance or other ingredients added. Add this amount to a gallon of water.
Add the gallon of bleach solution to the water tank. Do not pour undiluted bleach into the tank. Top off the tank with more water. Drive your RV a bit to allow the solution to move around in the tank.
Run the water through each faucet in the RV so that all lines are flushed with the chlorinated solution in the tank. According to CampingWorld.com, running about 6 quarts per faucet should be enough. (See References 2.) Do not use or consume this chlorinated water.
Flush the hot water faucets even more to make sure the old water has been purged from the hot water tank and is replaced by the bleach/water solution.
Allow the solution to sit in the tank for 3 to 6 hours. Or, ideally, let it sit overnight.
Drain the entire system, including the hot water tank.
Fill the tank with water again. Add ½ cup of baking soda in a gallon of water and place it in the tank to help remove the chlorine odor from the system. Fill the tank with fresh water.
Allow the solution to sit in the tank for a few days, if possible.
Flush baking soda solution from all faucets and drain water from system.
Fill with fresh water.