If needed, cook your chicken fully until the internal temperature reaches 165º Fahrenheit, then shred.
Distribute the shredded chicken amongst each tortilla, placing it in a strip down the middle. Repeat the process with the corn and one cup of shredded cheese. Roll each tortilla and place it into a 9 x 13" baking dish with the seam side down.
Next, melt the butter in a saucepan. Add the flour and whisk over low heat until a thick paste forms and no dry flour remains. Heat for 1 minute, but don't allow it to burn.
Into the paste, slowly add the chicken broth, cream of chicken soup, and sour cream and whisk until smooth. Stir in the green chiles, salt, and pepper.
Heat over low heat for 5 minutes. Pour the sauce over the prepared tortillas in the 9 x 13" baking dish. Top with the remaining two cups of cheese. Bake for 20 to 25 minutes or until the cheese is melted and bubbly.