Preheat the oven to 350 degrees Fahrenheit and grease a muffin tin with nonstick cooking spray or line with muffin liners.
In a stand mixer beat together oil and sugar until just combined then add the egg and beat again.
Add the gluten free flour, baking powder, baking soda, and salt to the mixture and beat on medium speed until a smooth but thick batter forms.
Gradually and slowly on low speed add the milk until incorporated. Scrape the sides of the bowl and beat until batter is smooth.
Fold in the blueberries with a spatula and scoop the batter into six muffin tin cavities all the way to the top. Add a small amount (less than a teaspoon) of jam to each top and swirl in with a toothpick. Top each muffin with some crumble mixture.
Bake muffins for 26 to 28 minutes until the tops don't cave when gently pressed and a toothpick comes out clean.