Most breads are leavened with yeast, which is killed during baking. If my recipe is flour, water, yeast, and a bit of salt, is the resulting bread non-vegan?
Yeast is a unicellular organism, a type of fungus (not an animal).
It is significantly less complex than any plant.
It has no central nervous system.
I eat it with a clear conscience.
Water, yeast, and salt are all vegan ingredients.
Flour could be non-vegan if it was bleached by an animal product (usually bone chars). This excludes every non-white flours, every white flours that were not bleached, and every white flours that were bleached by an inorganic chemical oxidant, such as potassium bromate.
So, answering your question: if you are not using bleached white flour, it is vegan. If you are, then it is likely to be vegan, but the only way to tell for sure is finding out how the flour was bleached.
Yeast, like mushrooms, are eukaryotic micro-organisms, which are part of the fungi kingdom, so yeast is not biologically classified as an animal and is thus vegan-friendly.
There are of course other things in bread that may be non-vegan such as butter and milk.