Yes, the frizzen should fly all the way open when you shoot...
First I would remove the lock and try, I have seen some flintlocks that were not inletted properly and the main spring was actually in a bind...Anyway, remove the lock and see if the frizzen opens all the way...If it works properly off the gun, you need to use lamp black on the back of the lock and remove the wood that is interfering...
If that doesn't work, try putting the flint in with the bevel up, so it hits the frizzen at a higher location...
If that doesn't work, fashion a wrap for the flint made of lead, just take a round ball, flatten and cut to fit...this adds a little weight and makes the flint more rigid in the cock...I actually make my wraps longer than most and drill a 1/4 hole in it so I can wrap it around the cock screw, so the wrap can't fall out when replacing the flint in the field...
If none of these work, you are looking at re-tempering the frizzen spring so it is softer or re-tempering the main spring so it is harder or bending the cock to change the angle that the flint strikes the frizzen so it scrapes instead of digs into the frizzen.