Grease two 8 inch cake pans with oil or butter and line the bottoms of each with a circle of parchment paper.
If your jam is cold and firm, add it to a glass bowl and microwave for 10 seconds. Add the lemon juice and whisk until it is loosened up. Set this aside for later.
Preheat the oven to 350 degrees F (177 C). In medium-large bowl, whisk the GF flour, salt, baking powder, and nutmeg together.
In the bowl of a stand mixer (or a large bowl and use a hand mixer) using the whisk attachment, mix the sugar and oil together. Add the eggs and mix on high for a few minutes until light and fluffy. Add half of the dry mixture and mix until smooth. Add the vanilla and half of the milk and mix until combined. Add the rest of the dry mixture and mix until smooth. Scrape the sides and bottom of the bowl with a spatula. Add the remaining milk and give the batter one last good mix.
Add enough batter to cover the bottoms of both cake pans. Drop 5 teaspoons of the blackberry jam mixture across the surface of the batter. Gently swirl the jam with a knife/skewer into the batter. Repeat with the other cake pan.
Evenly distribute the remaining cake batter between both pans. Repeat step 5 with the remaining jam mixture. Bake the cakes for 25-35 minutes or until a toothpick comes out clean or with some moist crumbs attached. Let the cake layers cool completely at room temperature.