First, I think you mean Rick Mayotte and that this is the video you watched for inspiration -
I assume that you understand that the intersection between the two cuts that Mayotte made at the end of his tool is the cutting edge. It needs to be sharp, but all it takes is a few swipes across the shorter of the two cuts with a diamond card to clean up and sharpen that edge.
Second, I suspect the problem is not in making the tool, but in how you are using it. The most likely cause of burning when using a parting tool is that as the tool cuts deeper into the wood, it binds against the wood, causing friction that burns the wood.
The secret to using any parting tool is to not try to part off entirely in a single pass. Instead, start the cut and go in a few mm, then start a second cut about half the width of the tool away from the second cut. Make that cut about twice the depth of the first cut. Then move the tool back to the first cut, and go in even deeper. Alternate between the two cuts until you complete the parting cut.
You can use a narrow parting tool to make a narrow groove in the surface of a turning, but if you need a deep groove, or if you need to part off, then the widtth of the cut will have to be greater than with width of the parting tool to avoid having the tool rub against the cut surface and cause burning.