Place cucumbers onto one end, slice in half down the length to create and x-shape, leaving the last 1/4-inch uncut; place into a bowl. Combine 8 cups water and sea salt in a saucepan over medium heat; bring to a boil. Pour brine mixture onto the cucumbers; brine until flavors combine, about 1 hour.
Combine red pepper flakes, 1/2 cup water, fish sauce, sugar, garlic, ginger, and fermented shrimp in a bowl; mix until sauce is thoroughly combined.
Rinse cucumbers in cold water; place in a colander to drain. Sit until semi-dry, about 10 minutes.
Lather cucumbers with sauce, inside and out, making sure to stuff the x-shaped cut as well. Place cucumbers, chives, radish, and sesame seeds in an air-tight container. Let sit at room temperature until flavors combine, 1 to 2 days; refrigerate until ready to serve.