Make the salsa verde. Rinse the tomatillos and place them in a small saucepan with the onion wedges, serrano, and garlic cloves. Cover with cold water. Bring to a simmer over medium heat for 10-15 minutes, until the tomatillos are soft and yellow-ish in color. Use a slotted spoon to transfer the tomatillos, onion, serrano, and garlic to a blender with the cilantro and lime juice. Blend until smooth, using some of the simmering liquid to thin out the sauce until it’s smooth and pourable. Season with salt and pepper.
Make the filling. In a mixing bowl, combine the chicken, half of the thinly sliced onion, 1/2 cup of the salsa verde, the Oaxaca cheese, and the ground cumin. Mix well and season with salt and pepper.
Roll the flautas. Wrap the tortillas in stacks of 4-5 in a damp paper towel and microwave for 1 minute, just so the tortillas are flexible and easy to work with. Lay a tortilla on a clean work surface, fill with 3 tablespoons of chicken filling and roll tightly into a log and secure lengthwise with a toothpick or two. Repeat with the remaining tortillas and filling.
Fry the flautas. Heat about 1/2 inch of canola oil in a deep-sided skillet over medium heat. Once the oil is hot and shimmering, about 350°F, add 3-4 of the flautas to the skillet (work in batches so as not to overcrowd the pan) and fry for 3-4 minutes per side, until golden brown. Lift the flautas out of the oil with tongs and let the excess oil drain off before laying them on a paper towel-lined plate. Season them lightly with salt. Repeat with the remaining flautas.
Serve. Lay the flautas on a bed of salsa verde and top with the remaining thinly sliced onions. Drizzle with mexican crema and top with cilantro and crumbled cotija.