Trim the cut end of the asparagus spears, and cut them into 3 inch lengths. Place them in a large bowl with 1/3 cup salt, and cover with water. Let stand for 2 hours. Drain and rinse under cool water, and pat dry.
Sterilize two pint size wide mouth jars in simmering water for 5 minutes.
In a saucepan over medium heat, combine the vinegar, sugar, 1 teaspoon of salt, mustard seed, dill seed and onion rings. Bring to a boil, and boil for one minute.
Pack the asparagus spears, tips up, in the hot jars leaving 1/2 of space from the rim. Tuck one dill sprig into each jar, and sprinkle in 1/4 teaspoon of red pepper flakes. Pour hot pickling liquid into the jars, filling to within 1/4 inch of the rim. Wipe rims with a clean damp cloth, and seal with lids. Process in a boiling water bath for 10 minutes.
Cool to room temperature. Check seals when cool by pressing the center of the lid. It should not move. Label and date; store in a cool dark place. If any jars have not sealed properly, refrigerate and eat within two weeks.