Does it have flaws? Yes, because humans aren't good at self-invoking or sustaining powerful emotions for long periods of time.
Could it still work? Yes, as many books/movies/TV shows have proven.
There are two big and closely related flaws in this system:
Humans can't sustain strong emotions for long periods
Humans aren't really built for long marathons of powerful emotions. Think about the last time you stayed angry - really and truly angry, not just a resentful simmer - about something. How long did that fierce anger last, before it faded into something milder? Typically, powerful anger only lasts a very short amount of time immediately following whatever caused the anger. Likewise, bursts of fear, love, hate, and other powerful emotions are just that: bursts. So your mages would only be able to perform powerful feats of magic if they had just then been provoked into a fierce burst of emotion.
Even if you could find a mage who could sustain a simmering rage for hours or days on end, they'd quickly burn themselves out, emotionally. Think about watching the most intense non-stop action sequences you can imagine, for hours or days at a time. After a while, you'd stop being excited - you'd just be bored. Humans tend to adapt to their environment, so even if you tried to create an environment that allowed you to sustain powerful emotions, you'd find that your mind will eventually try to balance itself back out.
Which leads to the second flaw:
Humans naturally seek emotional balance
Related to the first point, human psychology tends to look for emotional equilibrium, sometimes referred to as catharsis. That's why movies, books, and TV shows are structured the way they are, with scenes of quiet talking after wild action sequences, light-hearted comedy after intense drama, and so on. Our brains look for ways to find balance in our emotions, so if you try to make yourself angry enough for long enough, it's even odds that you'll instead start to find it funny - that's your brain looking for catharsis. For a similar reason, it's very difficult to inspire a burst of powerful emotion in yourself - as mentioned above, you'd need something to provoke you, because otherwise your brain moderates your reaction.
Various illnesses, such as depression or bipolar disorder, muck with a person's brain chemistry and suppress some of that balance-finding. So you could maybe get some serious power out of someone who's suicidally depressed, because their brain is literally malfunctioning to allow them to sustain that kind of powerful despair (although not all people with mental illnesses feel powerful emotion; in some cases apathy is a symptom of depression).
All that said...
As has been mentioned in comments, this is a fairly popular idea in works with magic users. In The Dresden Files, for example, it's one of the driving forces of magic. (You ever want a wild ride, try reading the book wherein the wizard asks a succubus to kiss him with all her power in order to inspire enough lust in him that he can use it to power a major defensive spell.) However, the wizard also points out the downsides of this - that once his burst of emotion is over, if he hasn't wiped out everything that was a threat to him, then he's left physically and emotionally exhausted (think how you feel after a long hard cry), with very little ability to work up enough emotion to cast any more magic.