Add pureed blackberries, lime juice, fresh ginger, soy sauce, and red pepper flakes to a small saucepan on the stove and stir well. Heat on high until mixture begins to bubble, reduce heat, and simmer for about 10 minutes.
Heat olive oil in a skillet over medium heat. Add shrimp and saute for 2-3 minutes per side, or until pink and cooked through. Toss shrimp with blackberry sauce and serve.
Notes
To strain out the blackberry seeds: place a fine mesh strainer overtop a clean bowl. Pour blackberry puree into the fine mesh strainer. Use a spatula or spoon to press and scrape the blackberry puree through the strainer, while the seeds remain in the strainer. Once there's mostly just seeds in the strainer, scrape any extra puree off the very bottom of the strainer and discard the seeds.