You can make these vegetarian with beans only if you wish. If you're an omnivore, make them with meat only, or make combo burritos with both meat and beans:
gluten-free flour tortillas (Trader Joe's Brown Rice Tortillas are good or you can try this recipe)
3 - 4 C cheese, grated (sharp or mild cheddars, monterey jack, or mozzerella usually work best)
1 - 2 C meat (cooked shredded or thinly sliced chicken, beef, pork or whole cooked shrimp)
4-oz can diced green chilis
1 diced onion
gluten free salsa (NOTE: Pace is NOT gluten free; many fresh salsas are)
sour cream (optional)
diced tomato (optional)
shredded lettuce (optional)
Saute the diced onion; add cooked meat and/or beans and saute just long enough to heat the mixture up. Add diced green chilis and/or salsa if you wish and cook about 1 minute longer. You can also experiment by adding small amounts of cumin or other traditional Mexican spices if you feel so inclined. What you add may depend on your choice of meat.
Place a tortilla in a pre-heated skillet on medium high heat. Heat briefly, just until warm and flexible. Place on serving plate, place 1/3 - 1/2 C meat and/or bean mixture on tortilla in a vertical strip and top with grated cheese.
Add other toppings at this point if you wish (salsa, sour cream, guacamole, diced tomato, shredded lettuce, etc.) then fold the bottom of the tortilla up over about half the filling, then fold the top down, fold the left side over, then the right to completely wrap the filling in the tortilla.