Start by placing a burrito-size flour tortilla on the counter or on a large cutting board. Place rice, black beans, and shrimp in the middle of the tortilla, vertically leaving about 1 inch of tortilla in the top and the bottom.
Add shredded lettuce, pico de gallo, sliced avocados, and a drizzle of aioli over the shrimp.
Fold one side of the tortilla over the filling. Rotate it so the filling is now horizontal. Fold the left and right sides of the tortilla over and roll the rest of the way up.
Wrap the burritos in wax paper for easier eating and storing.