Cook the noodles according to package directions, drain, and toss with a little oil so they don't stick. Set aside.
Whisk together the soy sauce, rice vinegar, sesame oil, sugar, and cornstarch slurry in a small bowl.
Pat the squid dry with paper towels.
Heat 1 tablespoon oil in a wok over high heat until just smoking. Add the squid and stir-fry 60 to 90 seconds until opaque. Remove to a plate.
Add the remaining oil, garlic, and ginger and stir-fry 15 seconds until fragrant.
Add the kale in batches, tossing constantly, and cook 2 to 3 minutes until just wilted.
Add the noodles and sauce, tossing to coat, and cook 1 minute until the sauce thickens.
Return the squid to the wok, toss briefly to combine, and serve immediately.