In a medium bowl, whisk together the light mayonnaise, Dijon mustard, and Major Grey's chutney until smooth.
Add the cooked chicken pieces, diced celery, sliced red onion, diced apple, halved grapes, and chopped parsley to the dressing; season with salt and pepper and stir to combine. Chill until ready to use.
Preheat the oven to 350°F (175°C) for the spicy pecans.
In a medium bowl, combine the pecan halves, melted butter, Worcestershire sauce, cayenne pepper, ground cumin, and 1/4 teaspoon salt; toss to coat evenly.
Spread the coated pecans in a single layer on a baking sheet and bake for 10 to 12 minutes, stirring once or twice, until toasted and fragrant. Watch closely to avoid burning. Remove and let cool.
Stir the cooled spicy pecans into the chilled chicken salad.
Lay out the flatbreads and divide the baby spinach among them. Spoon the chicken salad onto each flatbread, roll up tightly, and cut each wrap in half to serve.
