Spread the mirlitons in 1 layer in a strainer set over a bowl and sprinkle with salt. Let sit until they release some of their water, about 20 to 30 minutes.
Combine the drained mirlitons, bell pepper, jalapeno, green onions, and parsley. In a separate bowl, whisk together the vinegar, oil, sugar, and red pepper flakes. Pour the dressing over the mirliton and mix well. Adjust seasoning, to taste, with salt and pepper.