Combine blueberries, strawberries, raspberries, sugar, water, and butter in a small saucepan. Bring to a boil and cook until berries break down, about 5 minutes. Reduce heat to medium and continue to simmer mixture, stirring occasionally, for 5 minutes.

Remove from heat and allow to thicken until consistency is similar to a chutney or thick jam, adding flour to thicken even more if desired. Serve warm or chilled.