Hello Taylor,
I put your image into NI Vision Assistant and played around with it for a little bit. I think that if you want to capture defects on the order of what you've posted, you're going to need a better image if you want your code to work reliably.
I would suggest trying a few alternate lighting and filter combinations. It might also help if your camera was square to display you are inspecting.
One way of "seeing" the burr is to run a Histogram line as close to your part edge as possible. Doing so, you can clearly see the the dip in the graph where the burr is. The tricky part here would be to place that histogram line reliably from one part to the next. The rather "soft" edges on your current image make this difficult.