Arrange chicken in a large crockpot and cover with salsa. Cook on high for 2-3 hours until it shreds easily. You can also simmer chicken in salsa on the stovetop in a large pot until it reaches 165°F.
When chicken is almost done cooking, make rice on the stovetop according to package instructions (or you can also make oven baked rice, but start earlier because it takes longer). You'll make 1 & ½ cups of uncooked rice which will create about 3 cups of cooked rice to add to the crockpot. You can also make rice a day in advance and store in the fridge.
Finely shred chicken (burritos are easier to eat if chicken is shredded into small pieces). I usually shred mine right in the crockpot but you can take it out, shred on a cutting board, and return to the crockpot. Do not drain any of the salsa juices.
Add cooked rice and taco seasonings to the chicken and salsa mixture and stir until well combined.
Wrap tortillas in damp paper towels and microwave them for 1-2 minutes until they become more pliable. This step is important as the tortillas will crack when rolling burritos if they're not softened.
Spread 1-2 tablespoons of refried beans in the middle of a warmed tortilla. Top with about ⅔ cup chicken and rice mixture and ⅓ cup shredded cheese.
Roll tortilla around fillings to create your burrito and then wrap in a large sheet of parchment. I recommend nice, big parchment sheets as they make wrapping so much easier. I cut mine into 15x15 inch squares! You can also buy pre-cut parchment squares.
Place parchment wrapped burritos in a Ziploc bag or empty tortilla bag. Refrigerate up to 3-4 days or freeze up to 6 months.
From refrigerated: microwave in parchment paper, on high, for 2-3 minutes flipping halfway through cooking. From frozen: microwave in parchment paper, on high power, for 4-5 minutes flipping halfway through.
