Preheat grill to medium-high or preheat broiler. Combine chipotles, oil, garlic powder and cumin in a small bowl. Combine water and quinoa in a medium saucepan. Bring to a boil, reduce heat to low, cover and simmer until tender and most of the liquid has been absorbed, 15 to 20 minutes. Fluff with a fork.
Oil the grill rack or a rimmed baking sheet, if broiling. Season chicken with salt. Grill the chicken for 5 minutes or broil on the prepared baking sheet for 9 minutes. Turn, brush with the chipotle glaze and continue cooking until an instant-read thermometer inserted in the thickest part registers 165F, 3 to 5 minutes more on the grill or 9 minutes more under the broiler. Transfer to a clean cutting board. Chop into bite-size pieces.
Assemble each burrito bowl with 1/2 cup quinoa, 1/2 cup chicken, 1/2 cup lettuce, 1/4 cup beans, 1/4 avocado, 1 Tbsp salsa and 1 Tbsp cheese. Serve with 1 lime wedge.