Whisk the flour, flaxseed, baking powder, nutmeg and cinnamon together in a bowl until evenly blended then set aside.
Beat the eggs and sugar together in a separate bowl then whisk the buttermilk and 2 tablespoons of vegetable oil into the egg mixture. Stir the flour mixture into the egg mixture until no lumps of flour remain and the dough is firm enough to handle. Cover the bowl and refrigerate at least 10 minutes.
Roll the dough to 1cm thickness on a generously floured surface. Use a floured donut cutter to cut donut shapes out of the dough. Let the donuts stand for 5 to 10 minutes as the oil heats.
Heat the frying oil in a deep-fryer or large saucepan to 180 degrees C.
Fry the donuts in the hot oil in batches until golden brown on both sides, about 2 minutes per side. Drain on a paper towel lined plate before serving.