Make hibiscus syrup: Combine water and dried hibiscus flowers in a small saucepan. Bring to a boil, then reduce heat and simmer for 10 minutes.
Strain out flowers, add sugar, and stir until dissolved. Cool completely before using.
Prepare your glass: Chill a coupe or rocks glass in the freezer or by filling with ice water.
Mix the cocktail: Add gin, lemon juice, hibiscus syrup, simple syrup, and egg white (if using) to a cocktail shaker.
Dry shake: Shake vigorously without ice for about 15 seconds to create foam.
Wet shake: Add ice cubes to the shaker and shake again for 10-15 seconds until well-chilled.
Strain: Double-strain into your chilled glass to ensure a smooth texture.
Garnish: Float a dried hibiscus flower on top or add a lemon twist.