Combine hibiscus, 1/3 cup sugar, the cinnamon sticks, and 2 cups water in a medium saucepan. Cover and bring to a boil over medium heat. Reduce heat and simmer 5 minutes. Remove from heat and let infusion sit, covered, 20 minutes.
Meanwhile, in a blender, purée halved berries with remaining 1/3 cup sugar and 2 cups cold water. Strain into a metal bowl and stir in lemon juice. Set in a bowl of ice and water until cold.
Strain hibiscus infusion into another metal bowl and set in a bowl of ice and water until cold. (Discard soaked hibiscus, or see "Hibiscus flowers," below.) Combine hibiscus infusion and berry purée in a pitcher.
Fill glasses with ice. Add 1 1/2 oz. vodka to each if you like, followed by about 3/4 cup berry cooler. Stir in a splash of sparkling water. Top with quartered berries and mint.
Hibiscus flowers: Try leftover hibiscus flowers as a snack with a glass of mescal, as they do in Mexico. Pat the drained, soaked hibiscus very dry. Deep-fry in vegetable oil, a big spoonful at a time, until dark purple but not black (30 to 45 seconds at 375°); drain and sprinkle with salt.
*Find dried hibiscus, called jamaica in Spanish, at well-stocked grocery stores with Latino foods, at Latino markets, and at worldspice.com.
Make ahead: Through step 3, chilled, up to 1 week; stir before using.