The tragic case of Richard in Shakespeare’s Richard II is quite tricky and ambiguous. We can definitely identify some tragic hero qualities in Richard. Let us look at them first.
Richard is the king of England. So he inevitably enjoys a high, noble birth status.
Richard is also a fallen character. His tragic flaw seems to be his indecisive, ignorant and, in fact, incompetent nature. He lacks the sound judgment of a king.
He is not evil or villainous, but his poor and ineffective management of affairs of his state makes everybody dislike him. He also steals the wealth and property of his uncle John of Gaunt that belongs to his cousin Bolingbroke. As we know, this unrighteous deed becomes an indirect reason of his downfall as it provokes Bolingbroke to raise an army against him.
Lastly, like a typical Shakespearean tragic hero, Richard dies in the end also.
Certainly King Richard falls from divine grace. But there’s almost nothing in Richard’s character that makes him worthy of our respect and admiration. The audience hardly sympathizes with his downfall and tragic death in the end of the play. Of course, we can still say that he gets more punishment than he deserves.
Although much of the play’s action is focused on him, he doesn’t really enjoy being the central character of the play like other Shakespearean tragic heroes (Macbeth, Hamlet, King Lear etc.). Henry Bolingbroke, Richard’s cousin, comes out as a very important character in the play and competes for the position of the protagonist. He faces treachery and fights for justice. He becomes victorious and gets the throne.
Making the case of Richard so special and different from the usual tragic hero trend, Shakespeare leaves us with so many doubts. Whether Richard fits to be a tragic hero is actually a critical literary debate. So your question can have different answers.