In a wide bowl, mix flour + flax with fork. Whisk milk in gradually. Rest mixture 15 minutes.
Whisk mixture once more, then whisk in nutritional yeast, vanilla, sugar + cinnamon.
Heat a griddle or skillet over medium and add butter (or spray), letting it melt completely and coat the pan.
Soak brioche slices on each side, then place in warmed pan. Cook until golden brown, about 1 - 2 minutes per side.