Combine the Distilled White Vinegar (1 1/4 cup), Kosher Salt (3 tablespoon), and Granulated Sugar (2 tablespoon) in a small non-reactive saucepan, such as stainless steel, glass or ceramic, over high heat. Whisk until the salt and sugar are dissolved. Transfer the liquid into a bowl and whisk in the Water (2 cup). Refrigerate the brine until ready to use.
Stuff the Kirby Cucumber (2 pound) and Fresh Dill (16 sprig) into two clean wide-mouth 1-quart glass jars. Add the Whole Coriander Seeds (2 tablespoon), Mustard Seeds (1 teaspoon), Garlic (6 clove), Crushed Red Pepper Flakes (1/8 teaspoon), and chilled brine into the jars, dividing evenly. If necessary, add a bit of cold water to the jars until the brine completely covers the cucumbers.
Cover and refrigerate about 24 hours, then serve. Cucumbers will keep in the refrigerator for up to one month.