Not knowing any better, I ended up with some flints with the peak on top.
To hold them more securely in the jaw, I glued two small snippets of leather to the normal piece that holds the flint.
They lay cross wise and on either side of the peak when in position. The extra leather makes up for the extra elevation of the unwanted point on the flint.
Super glue works great and fuses together in a few seconds.
I use worn out (for my metal polishing purposes) but still usable on flint,, E-Z Lap Diamond Hones for touching up the edge.
Even a 'fine' hone cuts flint like it's a file on brass. I leave it right in the jaw to do it and easily extend the life of the flint several times as it takes almost nothing off to re-edge it. A double bevel seems to help too.
Here I thought I was the only one that ended up with those triangle shaped flints...