For the base, add 1 cup tomato juice and kimchi to a blender. Blend on high until smooth, about 1 minute. Transfer to a large pitcher and add horseradish, lemon juice, Worcestershire sauce, and celery seeds. Cover and refrigerate for at least 8 hours or overnight.
For assembly, mix the kosher salt, celery seeds, and chili flakes in a small shallow plate or bowl. Rub a slice of lemon around the rim of each glass and dip into the salt mixture.
Add vodka to the tomato base and serve in highball glasses filled with ice. Garnish with celery stalks.