There is no rule that states a tragic flaw can't also be a sin. In fact, they often correlate. Pride is a sin, and it is the tragic flaw of many literary characters. Lust definitely does play a role in Proctor's downfall; if not for his lust for Abby and their resulting affair, then he and Elizabeth might have been spared.
I mentioned pride above, and think that it also applies to John Proctor. He has a lot of self-pride, and strong opinions about things. This does not make him friends in the town. He argues with their reverend, Parris, continuously, and also with the Putnam family. John's pride won't allow him to give in to their points, and prompts him to point out the flaws in others. His self-pride makes him loathe himself; he knows he has sinned and is unworthy, and can't find his way back. To cover, he acts defensive, and almost signs a confession that is a lie, because he feels he truly is a liar, and not a good man.
So, one of Proctor's downfall is definitely his relationship with Abby; for flaws that are more evident in his words and actions throughout the course of the play, you can look to pride or other character traits. I hope that helped; good luck!