Eyes flashing/glittering/sparking, etc. with anger is an attempt by authors to describe the way emotions show behind a person's eyes. Ever heard that old cliche "the eyes are the window to the soul"? It's because somehow you can often "see" some bit of the person's essence/emotions in their eyes. It's why one of the things people say makes it immediately apparent someone is dead is that "their eyes are lifeless."
It is VERY difficult to describe using physical context words exactly what it is we see in another person's eyes, and how sometimes you can just TELL what someone's emotional state is largely by the look in their eyes. What seems to resonate the most is that description of there being a gleam, or a glitter, a spark, or a flash of something in the eyes, hence why it has become a cliche in writing, as authors have said "hey, that description actually gives the impression of the phenomenon I'm trying to evoke an image of" they've stolen the wording, and now EVERYONE uses it.
In fact it is overused, because it is so short and easy to drop in and move on. People often default to that description as a way of telling you how another (usually non-POV character) is feeling without having to work at finding a more accurate phrase, even when in context what the character is feeling might be better displayed by some more obvious physical cues.
"Eyes flashing with anger" is a perfectly legitimate phrase, BUT it should probably be reserved for situations where it is actually appropriate. After all, though that little glitter of anger in the eyes may be there whenever someone get angry, it is not USUALLY the thing that clues you in. Especially because you may have to be especially observant or know the person really well to even notice it. Usually what tells you someone is angry is more direct physical cues like facial expressions, body posture, etc.
Some examples when you may wish to use this phrase: a) when your POV character is already looking directly into the eyes of someone they know well and therefore notices it before any other cues or b) the person who is angry is SO good at concealing their emotional response that the emotion behind their eyes when they first begin to feel angry is the only evidence of how they are feeling (and the term "flashed" usually implies they manage to stifle that initial reaction quite quickly as well). In this instance your main character must be observant enough to pick up on it; a less aware character may get a "sense" that the person is angry but not know why.