It is never recommended to put any kind of floor cleaner or other cleaning product in your steam mop. It can damage the machine and corrode the water chamber, and you may also risk voiding any warranty you may have on your steam cleaner. Manufacturers usually recommend only using distilled water in a steam mop as this can prevent the build-up of limescale.
Steam mops are usually effective enough at cleaning floors and killing bacteria without having to use floor cleaner. They use hot vapour dispensed at high pressure and a microfibre pad to remove dirt, sanitise floors and kill germs.
Floor cleaning products are best used and most effective with a standard mop, or a microfibre, flat or sponge mop.