Place a medium saucepan over medium heat.
Add the butter to the saucepan.
Allow the butter to melt completely.
Add the gluten-free flour blend to the melted butter.
Whisk constantly until the butter and flour are fully combined.
Continue cooking for 1 to 2 minutes, or until the mixture begins to bubble.
Gradually add the chicken stock while whisking continuously.
Continue whisking until the mixture is smooth and free of lumps.
Add the milk to the saucepan.
Whisk until the milk is fully incorporated.
Add the salt, garlic powder, onion powder, and black pepper.
Whisk until the seasonings are evenly distributed.
Bring the soup to a gentle simmer.
Cook for 7 to 8 minutes, whisking occasionally, until the soup has thickened.
Add the cooked, finely chopped chicken.
Stir until the chicken is evenly incorporated into the soup.
Continue cooking briefly, if necessary, until the chicken is heated through.
Remove the saucepan from the heat.
Serve immediately, or transfer the soup to a jar or airtight container for later use.
If storing, allow the soup to cool slightly before refrigerating.