Melt the butter in a medium skillet over medium heat. Add the onion and cook until softened, but not brown, about 5 minutes. Add the garlic and cook 30 seconds more, stirring constantly. Cool slightly.
Add the onion/garlic mixture (with the butter that’s in the pan), ground chicken, hot sauce, salt, and black pepper to a large bowl. Combine the mixture with your hands being careful not to over-mix, and divide it into 4 portions. Shape each into a ball and flatten into a patty.
Heat a nonskillet over medium heat and add enough avocado oil to lightly coat the bottom. Once the skillet is hot, add the burgers and cook until they’re cooked throughout, about 6 to 8 minutes per side, flipping once. (I like to cover the skillet with a lid to help contain the spattering oil, but leave the lid ajar so steam can escape, otherwise chicken has a tendency to be rubbery.)
Place the burgers on the buns and serve with the slaw on top.