Bring the wild rice and water to a boil in a saucepan over high heat. Reduce heat to medium-low, cover, and simmer until the rice is tender but not mushy, 20 to 45 minutes depending on the variety of wild rice. Drain off any excess liquid, fluff the rice with a fork, and cook uncovered 5 minutes more. Scrape into a mixing bowl, and refrigerate until cold.

Whisk the vinegar, mustard, sugar, salt, garlic, dried tarragon, black pepper, and red pepper flakes in a small mixing bowl until smooth. Pour the safflower oil into the dressing in a thin, steady stream while whisking vigorously until the oil has been fully incorporated into the dressing; set aside. Stir the chicken, celery, parsley, and green onion into the cooled wild rice. Stir in the dressing until evenly blended. Cover the rice mixture, and refrigerate 4 hours to overnight.

Bring a small saucepan of lightly salted water to a boil. Add the sugar snap peas, and cook uncovered until just tender, about 30 seconds. Drain in a colander, then immediately immerse in ice water for several minutes until cold to stop the cooking process. Once the peas are cold, drain and cut into 1-inch diagonal pieces. Refrigerate until ready to serve. Stir the peas and toasted almonds into the rice mixture just before serving.