Whisk vinegar, orange juice, Dijon mustard, orange zest, cumin, and red pepper flakes together in a bowl. Slowly pour olive oil into the orange juice mixture, whisking until thick and thoroughly combined. Season dressing with salt and black pepper.
Remove stems from each leaf of kale. Stack 3 to 4 leaves of kale and roll together. Finely slice kale leaves crosswise to create thin ribbons.
Combine sliced kale, persimmon, apple, orange, and pistachio nuts in a bowl. Add dressing and toss until well coated.