In a medium saucepan bring water to boiling. Remove from heat and add dried Jamaica or hibiscus flowers. Let stand 10 minutes. Add sugar, stirring until dissolved. Let stand 20 minutes more.
Strain flower mixture through a sieve, pressing flowers to extract as much liquid as possible; discard flowers. Stir in lime juice. Cover and chill 4 hours. Serve over ice. Makes about 6 (8-ounce) servings.
Prepare flower water as directed. Cover and chill for up to 3 days.