In a small bowl, combine chili powder, cayenne, garlic powder, and flour. Set aside.
In a heavy bottomed, large stock pot, heat the 1 tbsp of vegetable oil over medium-high heat. Add chicken cubes and brown on all sides. Add onions and jalapenos and saute for 4 to 5 minutes. Add garlic and saute for 1 minute more. Mix in flour/spice mixture, stirring frequently, for 2 to 3 minutes. Deglaze with chicken broth. Then add vinegar. Stir well to combine. Bring to a boil. Lower heat to medium-low and simmer for 20 minutes, adding additional chicken broth, if necessary, to keep meat simmering in liquid. Remove to a sheet pan and shred with 2 forks. Add shredded chicken back into pot, along with pinto beans, lime juice and half the cilantro. Cook until mixture is heated through. Remove from heat and allow to cool.
Preheat oven to 350 F degrees.
In a large, deep-sided skillet, heat vegetable oil to 325 F degrees. While oil is heating, prepare chimichangas. Fill bottom half of a tortilla with 3/4 cup of the chicken and bean mixture and 2 tablespoons pepper jack cheese (when filling tortillas, use a slotted spoon to scoop out chicken if mixture is a little liquidy). Lift the edge of the tortilla and roll it over the filling to secure it. Fold in both sides and continue rolling until you reach the opposite end. Secure with a 6-inch skewer weaved through the seam side of burrito. Repeat with remaining tortillas. Slowly lower chimichangas into hot oil and cook 2 minutes on each side or until golden brown. You can cook 4 burritos per batch. Remove from oil, drain on paper towels and keep warm in oven until all are cooked.
To serve, place a bed of shredded lettuce on each plate, then a spoonful of salsa. Place chimichangas on top and add a dollop of sour cream, sprinkle with diced tomatoes, and remaining cilantro to garnish. Serve immediately.