Read the article on Shooting and Tuning a flintlock, which you will find under " Articles", indexed towards the top of the INdex page of this forum, under Member resources. You will better understand how to mount the flint to get better sparking in any lock.
I too am NO fan of the cut agate flints. Some work, some don't. The problem is that the agate is cut with a saw, ignoring the natural fracture lines in the rock. The English flints, and those that Rich Pierce makes are knapped, and by the very process, follow the fracture lines of the rock.
You want the flint to strike the frizzen at a 60 degree angle, from the bottom for best sparking. The point of Impact should be between 60% and 66% of the distance UP from the bottom of the frizzen. That point allows the flint to scrape steel bits from the face, not gouge them out, and also allows the frizzen to pop open at the right moment to permit the sparks to be THROWN into the pan. Badly tuned locks merely allow the sparks to dribble down the face of the frizzen, and bounce into the pan, slowing ignition time, or causing a misfire. You don't want the edge of the flint to strike too low on the frizzen, or it won't open the frizzen. You also want to oil and lube the frizzen pivot screw or pin, before every shooting outing, and you also need to polish, and lube the cam that rubs against the frizzen spring, so that those two surfaces rub as smooth as glass. The only PURPOSE of the frizzen spring is to keep the frizzen closed in the event you decide to point the muzzle downward vertically. It should not resist the frizzen popping open. A good lock will cut steel from the frizzen with NO frizzen spring present in the lock.
Re: your pictures: Turn the flint in the top photo over, so that the bevel is up, not down. That should get the edge to strike the frizzen at the right location.
The T/C lock looks okay.
The bottom photo indicates you have cocked the agate flint in the jaws, and you need to mount that flint so that the top and bottom of the flint are parallel in the jaws.
If the flint has to be mounted forward, due to being short for the lock, then put a twig or stick carved to needed width behind the flint and in front of the cock screw to hold the flint forward. Don't try to hold the flint forward by doing what you have done here. A couple of strikes, and that flint will go flying out of the lock and be possibly lost, or damaged.