I just picked up a Pedersoli I was very surprised how fast the lock time is. I did a lot of reading and took my time loading correctly and it played off in a good first experience. Not new to muzzleloaders but new to flintlocks.
Oh oh - you're addicted to rock locks now.

Sounds like you're doing it right, as a well prepped flintlock works very well. Wiping the pan clean between shots with one of those small disposable alcohol swabs is my preferred method as well (buy a pack of 100 at a drug store for a few bucks). I also agree with the general advice of 3f up to .50 cal and 2f for larger, although that's not a hard and fast rule. Priming with 3f or 4f seem to work about the same for me, and there are articles claiming advantages to priming with coarser powder. I have primed with 2f and it seemed fine as well, but I feel better with 3 or 4.
If you're having good luck with the flint you are using, measure its size and buy more of the same. You can choose from knapped English flint, French amber flint or saw cut flints. All will work fine if properly mated to the lock. Striking angle is critical to good spark and flint life - you want the flint to scrape down the face of the frizzen, not slam into it. I shop at Track of the Wolf, but Dixie is another good choice and there are others.
There's lots of little details to know and learn about flintlock shooting. But once you have the basics down (sounds like you do) then all you "need" to do is shoot a lot and have fun!
Is it best to prime and fire a empty gun to clear the oil?
No. Do that, and you're cleaning again. Burning BP generates salts that attract and hold moisture = rust. A fired blackpowder gun needs to be well cleaned before storing, even if just overnight. Just swab the bore well with a few dry patches after cleaning, making sure to bottom out the patch at the breech and give it a spin to help wipe off the breach face. Take a look at the patch to make sure the breach face it is clean, remembering you'll never get a lily white patch out of a black powder gun. You can then wet wipe the bore with a non-petroleum based lubricant/protectant before storage (Ballistol is my choice, but there are others). Then dry patch it again before you load for your next hunt or range session.