What is the historical outcome of Texas v. Johnson?
It is hard to definitively determine what sort of impact this case has had on history as whole. I would argue that one impact of the case has been on the American political scene.
In the years since the Johnson decision, American politics have become much more polarized and angry. We have come to have a situation in which we have conservatives and liberals seemingly at each other's throats. One example of this is the "culture war" between the two sides. One aspect of the culture war has to do with patriotism and the correct ways in which to show it. This particular aspect of the culture war was exacerbated by this decision.
So, I would argue that the major historical outcome of this decision was to deepen the divide between liberals and conservatives in the US, helping to create the polarized situation we now have.