In a bowl, combine the salt with 4 cups of water. Add the sunchokes; let stand for 1 hour.
Drain the sunchokes and return them to the bowl. Add the onion and red pepper and toss. Transfer the vegetables to 2 heated, sterile, quart-size canning jars.
In a small bowl, stir the dry mustard powder and flour with 1/2 cup of water to make a paste. In a large saucepan, combine all of the remaining ingredients and bring to a boil. Whisk in the mustard-flour paste until smooth. Simmer until thickened, 10 minutes. Pour the hot liquid over the sunchokes and tap to release any air bubbles.
Cover the jars (not too tightly) and transfer them to a deep pot filled with very hot water. Boil the jars for 25 minutes. Carefully remove the jars from the water and let cool.