A tragic flaw is a quality in a character, most often the main character, that leads to his downfall. Under this definition, Romeo exemplifies several qualities that eventually end his life:
1. Romeo is deceptive. The Montagues and Capulets hate each other. Instead of facing this truth head-on, Romeo devises a plan to quickly marry Juliet without anyone's knowledge or consent (except the bride's). Because he devises this quick plan, the repercussions mount quickly and lead to both his and Juliet's deaths.
2. Romeo falls in and out of love quickly. Don't forget that when the play opens, Romeo is so grief-stricken over the loss of Rosaline that his moping is noted by various friends and family members. Consider this exchange in act 1, scene 1:
What sadness lengthens Romeo's hours?
Not having that, which, having, makes them short.
Out of her favor, where I am in love.
This "her" is Rosaline. Yet mere hours later, he has spotted Juliet and has, once again, fallen helplessly in love. Less than twenty-four hours later, he is married to an entirely different woman than the one he was originally in love with by his own admission. Even if Rosaline declined his sentiments and even though fate has seemingly brought him to Juliet, the space to grow a new relationship needs time that Romeo doesn't allow. This flaw leads to Romeo's downfall.
3. Romeo doesn't think things through. Romeo marries Juliet on an impulse, even though he knows their families will not be happy. Surely such a weighty decision deserves more than a few hours' consideration. In an earlier scene, we see him first declining to fight Tybalt because he is Juliet's family. (And since she is his new and secret bride, this is even more complicated.) Moments later, after Mercutio steps up to defend Romeo's honor and dies, Romeo flies into action after all and kills Tybalt. This leads to his banishment and eventual death. And, of course, there is the final scene where Romeo finds Juliet and ends his own life. Although he notes that she still looks "yet so fair," he doesn't stop to process that perhaps she isn't dead after all; he simply jumps to his next step—suicide. Romeo's impulsivity throughout the play culminates in this scene and greatly adds to the angst of the audience.
Romeo, a character who loves deeply, acts without thinking, and deceives those around him, is nonetheless a character who is also somehow deeply relatable and even idolized. In the end, he is willing to risk it all for the ability to love freely and without constraints.