Cut the potatoes lengthwise into ¼-inch x ¼-inch thick slices. Put the fries into a large bowl of cold water and refrigerate for at least 1 hour.
Heat a deep-fryer or a large heavy-bottomed pot filled with enough oil to reach at least 3-inches up the pot over medium heat to 350ºF (180ºC). In a medium mixing bowl whisk together the flour, salt, garlic powder, paprika, pepper and cayenne. Slowly add enough cold water to form a thin batter, about 1½ cups. Dip the fries in the batter and add to the oil. Fry until golden brown and crispy, about 5 minutes. Remove to a paper towel lined plate to drain.
For the grilled chicken:
Rub the chicken with the olive oil then season with salt and pepper on both sides. Heat grill to medium-high heat. Add the chicken to the grill and cook until browned and char marks start to appear, about 5 minutes. Flip and continue to cook until the chicken is browned and just cooked through (or reaches an internal temperature of 165ºF/ 73.8ºC), about an additional 4 minutes.
Remove to a cutting board and let cool. Chop the chicken into 1-inch cubes and set aside.
For burrito assembly:
Heat a large nonstick skillet over medium heat. Working one at a time add a tortilla to the pan and sprinkle 1 cup of the cheese over the top, cooking until the cheese just melts. Remove to a clean workspace and add the lettuce, half of the chicken, slices of avocado, ¼ cup of the pico de gallo and a handful of fries.
To assemble the burrito, fold the bottom half over the top half then pull the tortilla back to form the filling into a roll. Fold one side in then the other, then tightly roll the burrito.
Add the burrito, cut side down to the skillet and cook until golden brown, about 2 minutes. Flip and brown the other side, about another 2 minutes. Remove and cut in half then serve immediately. Repeat with the remaining tortilla and ingredients.