Toast the slice of sourdough bread in a toaster until golden brown, about 2-3 minutes. Spread the softened butter evenly over the warm toast.
Fill a small saucepan with 2 cups of water and bring to a gentle simmer over medium heat. Add the white vinegar to the water.
Crack the egg into a small bowl. Gently slide the egg into the simmering water, swirling the water to help it hold its shape. Cook for 3-4 minutes for a runny yolk or 5-6 minutes for a firmer yolk.
Scoop the avocado flesh into a small bowl and mash it with a fork until smooth but slightly chunky. Spread the mashed avocado evenly over the buttered toast.
Use a slotted spoon to carefully remove the poached egg from the water, letting excess water drain off. Place the egg on top of the avocado toast.
Sprinkle the toast with kosher salt, black pepper, and red pepper flakes (if using). Serve immediately.