Can people get "addicted" to anger?
In the broad not clinical sense, sure. Pavlov's dog, a child whose tantrums are rewarded gets what they want and it becomes habit. Or the classic,"to a man with a hammer everything looks like a nail" when that's the only tool they have. like other"addictions" it prevents you from being a well rounded person.
Yes :
" Anger can be an empowering and therapeutic emotion when released in a healthy way, but it can also be addictive. Just like individuals who seek thrills for the adrenaline rush, some people have the same effect from anger. Individuals can become addicted to endorphins they feel when they get angry. Like all “highs,” once the feeling wears off, individuals can feel anxious or depressed. This can cause someone to seek thrills in the form of drugs. Stimulants like Cocaine can provide excitement and can increase feelings of euphoria to replace anger. If someone can no longer acquire their substance of choice, he or she may revert back to angry feelings or develop a habit for emotional support. "
[addictioncenter.com]
[psychologytoday.com]
about the Emotional Hormones which are related to most of the addictions, you can find more info here : How Hormones Influence You