Preheat oven to 425 degrees and grease a baking sheet.
Dry chickpeas well by rolling underneath paper towels. Toss with 1 tablespoon of olive oil, turmeric, cumin, paprika, coriander, ginger, cinnamon, and a pinch each of salt and pepper. Roast 20 minutes, tossing around the pan midway through. Keep a close eye on them after 10 minutes of cooking to prevent burning. The chickpeas will crisp up a bit more when you take them out of the oven as well!
Meanwhile, make the chutney. In a bowl, stir together pineapple, mango, red onion, chili powder, cinnamon, garlic clove, lime juice, red pepper flakes, and a pinch of salt and pepper.
Lay a handful of arugula in each tortilla. Spoon in about 1/4 cup chickpeas and arrange avocado slices atop. Drizzle with chutney, squeeze some fresh lime juice overtop, and finish with a bit of Greek yogurt, as desired.