If the audience is trying to figure out Hamlet's tragic flaw from his "To be, or not to be" speech, they need to look no further than lines 85-88. Note the following words:
Thus the native hue of resolution / Is sicklied o'er with the pale cast of thought, / And enterprises of great pitch and moment, / With this regard their currents turn awry, / And lose the name of action.
Proof for either tragic flaw (melancholy or inaction) can be found within these lines. The proof for the tragic flaw of melancholy can be found in the quotation about "the native hue of resolution" that is being "sicklied o'er with the pale cast of thought." In other words, it doesn't matter whether the scholar believes Hamlet is contemplating suicide or avenging his father because Hamlet is not able to do so due to his melancholic thoughts, sad musings, contemplation of wisdom in this arena, and simply the ideas in his head. If the reader is looking for proof of the flaw of inaction (or Hamlet's inability to act), one needs only point to the words "With this regard their currents turn awry, / And lose the name of action." Again, it doesn't matter in the slightest whether the reader thinks Hamlet is contemplating ending his own life or killing Claudius in order to avenge Hamlet's own dad; Hamlet can't commit murder no matter what. He is unable to act, period. The reasoning matters not. The question of "why" is not important. The flaw is not in the asking of "why," but in the fact that Hamlet is not able to act.