ZDoom

Oh awesome! Thanks for the link! I did not know that existed.

This can be done as a mod. (Here's one)

Most modern first person shooters flash the screen when taking damage, most including that to highlight whichever direction the damage was taken from.
This kind of a feature would be nice to see as it would be easier to tell when you get hit and from where.
Obviously it should be disabled by default but it would be nice for it to exist.