In a medium bowl, whisk together the light mayonnaise, Dijon mustard, and Major Grey's chutney until smooth.
Add the diced cooked chicken, diced celery, sliced red onion, diced apple, halved grapes, and chopped parsley to the dressing; season with salt and pepper and stir until evenly combined. Chill until ready to assemble.
Preheat the oven to 350°F (175°C) for the spicy pecans.
In a medium bowl, toss the pecan halves with melted butter, Worcestershire sauce, cayenne pepper, ground cumin, and 1/4 teaspoon salt until evenly coated.
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; be careful not to burn them. Let cool.
Combine 1 cup of the cooled spicy pecans into the chilled chicken salad, reserving any extra for topping.
Lay out the 4 flatbreads and divide the baby spinach evenly among them. Spoon the chicken-and-pecan mixture onto each flatbread, roll tightly, and cut in half to serve.