Bring 1 gallon water to a boil in a large pot and dissolve pickling salt in the boiling water. Place cucumbers, onions, cauliflower, red bell peppers, and apples into a large bowl or crock and pour the boiling water over the vegetables. Allow to stand overnight and drain the next morning.
Transfer vegetables to a large stock pot and mix in sugar, vinegar, 3 cups water, flour, dry mustard powder, and turmeric until thoroughly combined. Bring the relish to a boil and reduce heat to medium-low; simmer until vegetables are cooked through and soft, about 20 minutes.
Sterilize the jars and lids in boiling water for at least 5 minutes. Pack the relish into the hot, sterilized jars, filling the jars to within 1/4 inch of the top. Run a knife or a thin spatula around the insides of the jars after they have been filled to remove any air bubbles. Wipe the rims of the jars with a moist paper towel to remove any food residue. Top with lids and screw on rings.
Place a rack in the bottom of a large stockpot and fill halfway with water. Bring to a boil and lower jars into the boiling water using a holder. Leave a 2-inch space between the jars. Pour in more boiling water if necessary to bring the water level to at least 1 inch above the tops of the jars. Bring the water to a rolling boil, cover the pot, and process relish for 15 minutes.
Remove the jars from the stockpot and place onto a cloth-covered or wood surface, several inches apart, until cool. Once cool, press the top of each lid with a finger, ensuring that the seal is tight (lid does not move up or down at all). Store in a cool, dark area.