In a small saucepan, combine the brown sugar, water and hibiscus flowers over medium heat. Bring to a simmer and stir until the sugar has completely dissolved and the flowers have rehydrated, 3 minutes. Remove from the heat and let the mixture steep while it cools. Once cool, strain the syrup into a blender, discarding any solids.
To the blender, add the remaining ingredients, except for the sparkling wine, and purée until smooth.
Pour into ice pop molds and freeze until solid, 4 to 6 hours.
Run the molds under room-temperature water for a few seconds to release them, then place each ice pop into a glass of Prosecco or sparkling rosé, and serve immediately.