In a medium bowl, mash blackberries with sugar, using a fork. Let sit about 15 minutes for fruit to get juicy.
Stir in vinegar. Cover and chill, covered, 3 to 5 days for flavors to meld. Strain syrup and transfer to a jar.
For each serving, pour 1 oz. syrup into an ice-filled glass. Add 5 oz. sparkling water and stir to combine. Or combine all of shrub and sparkling water in a large, ice-filled pitcher. Top glasses with blackberries and add an herb or flower sprig.
* Find coconut sugar at well-stocked grocery stores. Kayne prefers a raw vinegar such as Bragg.
MAKE AHEAD: The shrub syrup, chilled airtight, up to 1 month.