Certainly don't want it resting on the frizzen. I don't think there's any official distance to set the flint from the frizzen face, some locks seem to be fussy about it, some not? On both my rifle and musket, both spark great regardless of the distance, within reason. On my Bess right now, the flint is about 3/16" away. I'll probably move that forward now that I noticed it, but it's working fine that way. ?? Same with my rifle.
Not sure about others, but I square my flint with/to the face by leaving the flint a bit loose, let the cock down gently until it touches, flint then "self aligns", gently pull it back and tighten her up. I suppose though, if you just put it on half cock and moved the flint forward until it touched, you could do it that way....if the lock will allow it. Even with the big old flint I've got in Bess now, if I moved it that far forward the jaws would have a poor purchase on the flint.
Anyhow, there is no "should" or "shouldn't" touch the frizzen, not touch, be 1/16" or 1/8th, or five foot from the frizzen face, etc., the lock will dictate what sparks best.
Yes, not exactly clear if the cock is stopping at half cock, or if the flint is missing the frizzen entirely?? Also, at half cock, does the cock "sit up straight", of does it "droop" forward? That seems to be a problem on many of those locks.