You can mix up the seasoning, dredge, and grill but, imo, that's not blackened fish (or chicken, if you wish). Captain's method, in a cast iron pan, is the only way to get it right.
Though you'll see, erroneously I think, recipes calling for a low temp setting followed by an increase, imo the best way is to stick your cast iron pan on a high burner and let it sit there while you get your fish or chicken ready (at least 10 min--it cannot be too hot). You don't want really thick filets; if you use chicken breasts remove the tenderloin and pound a bit to even out the thickness. I use clarified unsalted butter instead of oil (I like the flavor, and I really recommend it) but the end result is the same. Dip the filets in the clarified (or oil) first. Then dredge your filets in your mix as if you were coating them in flour; they should be completely covered. Shake off excess. Immediately lay in your filets--don't crowd them--and top with a few teaspoons of melted whole (not clarified) unsalted butter; cook in batches if necessary. Cook about 2 minutes till the underside is blackened; flip, pour on 2 teaspoons melted butter, and cook till blackened on the bottom. Remove to a hot platter.
If you don't have a good exhaust fan you'll smoke up your kitchen and set off your smoke detectors. If you have an outside burner, you might prefer doing it there.
I use Paul Prudgomme's original mix:
1 Tbls Paprika
2 1/2 tsp Salt
1 tsp Onion powder
1 tsp Garlic powder
1/2 tsp Oregano, dried
1 tsp Cayenne pepper
3/4 tsp White pepper
3/4 tsp Black pepper
1/2 tsp Thyme, dried
Make more if necessary, the above doesn't make much. When I do chicken I add a 1/4 tsp allspice and a 1/4 tsp cinnamon.