Bring water, white sugar, hibiscus, brown sugar, ginger, and lemon zest to a boil. Reduce heat and let simmer until sugars dissolve and flowers soften, about 10 minutes. Remove from heat and steep syrup until flavors combine, about 5 minutes.
Strain syrup into a container through a fine-mesh strainer, pressing solids with a spoon to extract as much liquid as possible. Discard solids.
