How can I deal with a significant flaw I found in my previous supervisor’s paper?
Two suggestions:


You found that someone was wrong in a good journal.  The fact that the error was published in a good journal does not mean that it is worth working on.  You should decide if this error is really worthy of your research efforts.  It might be better for you to work on something more important.
If you decide to pursue the error, you can choose to present your correction as a new idea.  If you tell people that you have found a new idea that advances the state of the art, that makes you look good.  If you tell people you have found someone else's error, that makes the other person look bad but may fail to make you look good.  The actual substance of the research can be the same, but the way you present it makes a world of difference in how it is viewed.