I would not put that in the dishwasher. There are phosphoric acid dishwasher cleaners available at the hardware store. If the hose or connection from the dishwasher is "gunked" up, just take it apart and clean it.
Just pouring your solution into the sink or disposer takes care of that line.
At the washing machine, is there not a standpipe where the hose goes? Pour it in there. If the machine drains to a deep sink, just put it there. As with the DW, if you suspect problems with the hose itself, take it apart. If the interior of the machine is messed up, then a new machine would cost less than the amount of enzyme it takes to fix it!