In a medium saucepan, combine the vinegar, 1 ½ cups water, the sugar, salt, jalapeno, and pepper flakes over medium heat and bring to a boil. Reduce heat to medium-low, and simmer gently until the salt and sugar have dissolved and the mixture is fragrant, 8 to 10 minutes. Remove from the heat and set aside to cool completely, then transfer to a large airtight container. Refrigerate until cold, about 1 hour.
Add the cucumber and radishes to the cold pickling liquid, making sure they are fully immersed, and refrigerate for at least 8 hours or up to 1 month before serving.
To make the bloody Mary mix:
In a spice grinder, combine the pepper flakes, cumin, coriander, celery seeds, and peppercorns and process to a fine powder. Pour the tomato juice into a large glass pitcher, add the spice mix, lemon juice, Worcestershire, and horseradish, and stir to mix well. Add the bay leaves, then season to taste with salt. Cover and refrigerate until ready to use, up to 5 days in advance.
To assemble the cocktails:
Have ready six pint-size glasses. add 2 oz vodka to each glass, then fill the glasses with ice cubes. Pour Bloody Mary mix to nearly fill each glass (about 5 oz or 2/3 cup), then add a dash or two of hot sauce to each glass. For each cocktail, spear an olive, 2 slices pickled radish, and an onion with a bamboo spear, then add to the glass. Grind some black pepper over the top and serve.