Add the yeast mixture to the bowl of a stand mixer along with the soaked flaxseed and softened vegan butter. Whisk to combine.
Add in the flour, salt, and 2 tablespoons granulated sugar. Use the stand mixer's paddle attachment to mix everything together at a medium speed. (Or use a wooden spoon to mix everything together by hand.)
Once the ingredients are combined and there are no dry ingredients visible, switch to the dough hook attachment and knead for 3-5 minutes at a medium speed. (Or turn the dough out onto a lightly-floured surface and knead 8-10 minutes by hand.)
Many factors can influence the hydration of the dough. If the dough is seeming overly sticky (sticking a lot to the sides of the stand mixer bowl, or to your fingers), gradually work in extra flour about 2 tablespoons at a time. Knead the extra flour in completely before assessing whether you need additional flour. The dough should be slightly tacky to the touch, but it should "clean" the sides of the stand mixer bowl. It should not stick excessively to your fingers or to your work surface.
You're done kneading when the dough is smooth and elastic — it should "bounce back" quickly if you poke it. If you poke it and a deep indentation remains, you should continue to knead.