Prep the chicken: Chop or shred cooked chicken. If starting raw, poach in salted water until 165°F (74°C), then cool completely and pat dry.
Make the dressing: Whisk the Greek yogurt, Dijon, lemon juice and zest, pickle brine, garlic powder, salt, and pepper in a large bowl.
Fold: Fold in the chicken, celery, pickles, red onion, dill, and almonds until evenly coated. Taste and adjust.
Roll: Warm the tortillas, layer lettuce, chicken salad, avocado, and cucumber, then roll tightly, wrap in parchment, and slice in half.