Whisk together ground flax and hot water in a small bowl. Set aside.
Whisk together sorghum flour, brown rice flour, baking soda, and salt in a small bowl.
Cream together shortening and sugars on medium high speed in bowl of stand mixer fitted with paddle attachment. Cream until a thick paste forms, about 30 seconds. Add flax mixture and vanilla. Cream until mixture is light and fluffy, about 45 seconds.