For the cordial; combine water and sugar in a saucepan, stir constantly over medium heat without boiling, until the sugar has dissolved. Bring to a boil, reduce heat and simmer for 5 minutes without stirring. Add the lemon juice and blueberries, simmer for 8 minutes. Remove from the heat and stir in the tartaric acid. Set aside to cool. Pour the mixture into a blender and blend until smooth. Strain, discarding the skins and refrigerate until cold. Once cold, pour into a clean sterilized jar and refrigerate for up to 1 month.
For the cocktail, pour the lychee and the syrup from the can into a snap lock bag and freeze for 4 hours until frozen.
Dip the edge of 4 cocktail glasses into egg white then dip in jelly crystals. Place the glasses into the freezer for 5 minutes. Add 160ml of blueberry cordial, gin, lime juice and frozen lychee and syrup into a blender. Blend until well combined. Divide between 4 martini glasses. Top with extra blueberries and edible flowers. Serve immediately.