I've had this problem before. Tonight my boy called with the same problem.............
I got him a bag of hand-knapped English flints. At least some of them have a sort of point or peak on one of the facets the hammer jaws grip down on. This leaves the flint more or less able to pivot around in there rather than being secured. He is using a leather in the jaws......... I could never get flints like that to hold, either.
If there is a trick, I haven't found it. When I order ten English flints, I usually get 6 that are nice and flat and 4 like you described. Some are worse than others... I either use them on the range or just throw them in my used flint pile.
Itís a very simple fix. Go to the Home Depot or Loweís and get a diamond dremel grinding drum. They are about $10. You donít aven need the dremel. Chuck it in a drill and it will make quick work of flattening the top of the flint.
Sometimes I'll get a flint like this when I order them online. I do as above and knock the high side down with a dremel tool. As long as the jaws of the cock can get a good grip, then you don't need to take much off, but a dremel works. When I go to places like Dixons gun makers fair, and somebody is selling flints, I will pick through the pile until I get flints that meet my specifications.