Remove the lock and see if the sear is going all the way into the full cock notch. If so. the sear bar might be resting on the bottom or side of the hole.
It looks like the sear bar could be binding against the set trigger. could that be the problem.
Absolutely. The sear bar must move freely. Put some spotting stuff on the sear bar and remove the offending wood or get more space between the triggers and the sear bar . Often the trigger blades are made tall. You can take some off.
Temporarily shim up the triggers and see how it works.
Put a wooden flint in the jaws for testing purposed. Never dry fire a flintlock, the cock will bend.
Added later, the sear bar should not bend, it is hard and heat treated. IF it did bend up that would make the problem better. IT is not a good solution though.