In a medium-sized skillet, combine the shredded chicken, diced green chiles, green chile sauce, ground cumin, and salt. Heat the mixture over medium heat, stirring occasionally, until thoroughly warmed, approximately 4 minutes.
Place the flour tortillas between damp paper towels and heat them in the microwave for 30 seconds to make them pliable.
Spread a layer of refried beans down the center of a warmed tortilla. Add a portion of the chicken mixture and sprinkle with shredded cheese. Fold in the sides of the tortilla, then roll it tightly into a burrito shape. Repeat this process with the remaining tortillas and filling.
Heat about 1 inch of cooking oil in a heavy-bottomed skillet over medium-high heat. Once the oil is hot, carefully place each chimichanga seam-side down into the skillet. Fry until golden brown, about 1 minute per side, rotating to ensure even crispness.
Transfer the fried chimichangas to a paper towel-lined plate to drain excess oil. Repeat with the remaining chimichangas.
Serve immediately with your choice of toppings, such as crema, guacamole, or fresh pico de gallo, to enhance the flavors. Enjoy!