Using a four-inch ring cutter, cut three tiny tortillas from each large tortilla.
Wrap the tiny tortillas in a damp paper towel and microwave until pliable, about 10 seconds.
In a small bowl, combine the flour and water and mix until smooth.
Arrange the tiny tortillas on a clean work surface. Leaving a half inch border, assemble the cheese, black beans, rice, and chicken in the center of each tiny tortilla, taking care not to overfill.
Roll each filled tiny tortilla into a chimichangita by folding two opposites borders slightly over the filling, then folding one border entirely over the filling. Spread a small layer of flour-water mixture over the remaining border, and finish rolling into a chimichangita. The flour-water mixture helps the chimichangita stay sealed.
Fill a large skillet with 1-inch of canola oil and preheat over medium heat. The chimichangitas should bubble immediately when placed in the pan. Fry the chimichangitas until deeply golden brown on all sides, about 8 minutes total. Reserve the fried chimichangitas on a baking sheet lined with a rack. Season with salt, to taste.
Arrange the warm chimichangitas in a basket and add a liberal amount of enchilada sauce. Drizzle with crema and scatter with black olives.