Heat sugar, 1 1/2 cups water, and hibiscus in a saucepan until boiling. Let cool for 1 1/4 hours, then strain, discarding hibiscus.
Chill until cold, at least 45 minutes and up to 2 weeks.
Combine hibiscus syrup, tequila, grapefruit and lime juices, vermouth, and bitters in a pitcher (at least 2 qt.).
Fill tall glasses with ice. Pour about 1/2 cup syrup mixture into each glass and top up each with about 1/2 cup club soda. Stir, then garnish with lime slices.
*Buy from a Latino market or from worldspices.com
Note: Nutritional analysis is per serving.