Place chicken tenders in a medium pot, cover with water, and bring to a boil over medium-high heat. Reduce temperature to medium-low; simmer until chicken tenders are cooked through, 6 to 8 minutes. Drain; transfer tenders to a cutting board and cut or shred as desired.

Heat oil in a skillet over medium heat; cook shallot until soft and translucent, about 5 minutes.

Combine cream cheese, ranch dressing, Buffalo sauce, and cooked shallots in a bowl until creamy. Stir in chicken; season with salt and black pepper.

Spread some Buffalo chicken mixture on 1 tortilla; top with some Gouda and Colby-Jack cheeses. Cover with a second tortilla; set aside. Repeat with remaining tortillas, chicken mixture, and cheeses.