Line a large baking sheet with parchment or waxed paper.
In a large mixing bowl, combine the chicken, cheddar, almond flour, egg, garlic, parsley, salt, pepper, and red pepper flakes. Use your hands to mix everything well.
Using 2 tablespoons at a time, form the mixture into small patties about 2 ½ to 3 inches across. You should get 24 to 26 patties. Place on the prepared baking sheet and refrigerate one hour.

Set a large skillet over medium heat and add 1 tablespoon of the oil and ½ tablespoon of the butter. Once hot, add 8 to 10 of the chicken patties. Cook about 3 minutes per side, until cooked through (the internal temperature should reach at least 165ºF on an instant read thermometer).
Place the finished patties on a paper towel lined plate to dry and repeat 2 more times, until all of the patties are cooked. Note: you may want to scrape out some of the baked-on cheese between batches, to avoid burning it.
Serve warm, with some ranch or bleu cheese dressing for dipping.