Cook squid in a 5-quart pot of well-salted boiling water, stirring once, until just opaque, about 1 minute. Transfer with a slotted spoon to an ice bath to stop cooking, reserving boiling water in pot.
Boil noodles in same water until just tender, about 3 minutes.
When squid is cool, transfer to a plate, reserving ice bath, and pat dry.
Drain noodles, then transfer to ice bath to stop cooking. Drain well, then snip with kitchen shears 2 or 3 times.
Meanwhile, whisk together lime juice, fish sauce, sugar, red pepper flakes, and 1 teaspoon salt in a large bowl until sugar has dissolved. Add oil in a slow stream, whisking until combined.
Add noodles and calamari to dressing with cucumber, scallions, and herbs and toss well.