In a medium saucepan, combine the vinegar, sugar, soy sauce, sake, kombu, bonito flakes and 1/2 cup of water. Bring to a simmer, whisking to dissolve the sugar. Turn off the heat and strain the sauce with a fine-mesh strainer.
Bring a large pot of salted water to a boil. Add the noodles and cook according to package instructions. Drain, return to the pot and toss with the rice vinegar sauce.
Combine all of the avocado purée ingredients in a blender until smooth.
Divide the noodles between bowls. Top with avocado purée, cucumbers, kimchi, scallions, cilantro and sesame seeds.