Combine strawberries and sugar in blender or food processor; liquefy. Turn out into a medium pot over medium heat and bring to a boil; reduce to low and simmer for 5-8 minutes, or until glossy and thick. Remove from heat and let cool to room temperature.

Meanwhile, bring coconut milk to a boil in a separate pot over medium heat; reduce to ½ cup, 15 to 20 minutes. Pour into a large mixing bowl and whisk in sweetened condensed milk; let cool to room temperature.

When ready to assemble, whip cream to stiff peaks. Fold one-third of cream into coconut milk mixture to lighten, then follow with the remainder of the cream; pour into a 6 to 8-cup-capacity serving dish. Spoon reserved strawberry mixture over and, using a spatula, gently fold in until marbled. Sprinkle coconut flakes over and freeze for 4 hours or until firm. Spoon or scoop into chilled bowls to serve.