Stir warm soy milk, honey, and brown sugar together in a bowl until sugar is dissolved; stir in yeast and let sit until mixture becomes foamy, about 5 minutes. Stir 3 cups flour, ground flax seed, butter, and salt into yeast mixture. Mix remaining flour, 1/2 cup at a time, mixing well after each addition, until dough pulls together.
Turn dough onto a lightly floured surface; knead until smooth and elastic, about 8 minutes.
Lightly oil a large bowl and place dough in the bowl, turning to coat. Cover with a damp cloth and let rise in a warm place until doubled in volume, about 30 minutes.
Carefully turn dough onto a lightly floured surface; punch dough down. Divide dough into 2 equal pieces and form into loaves. Place loaves into 2 lightly greased 9x5-inch loaf pans. Cover loaves with a damp cloth and let rise until doubled in volume, about 40 minutes.
Preheat oven to 425 degrees F (220 degrees C).
Place loaves in the preheated oven and reduce heat to 375 degrees F (190 degrees C); bake until the tops are golden brown and bottom of loaves sound hollow when tapped, 27 to 30 minutes.